Resourcesdown chevron
Testimonials
Plans
Sign in
Sign up
Resourcesright arrow
Testimonials
Plans
Bytelearn - cat image with glassesAI tutor

Welcome to Bytelearn!

Let’s check out your problem:

Solve. 6-6x^(2)=3x Choose 1 answer: (A) x=3,-(1)/(2) (B) x=(1+-sqrt17)/(-4) (C) x=(-4+-sqrt34)/(3) (D) x=(7+-sqrt193)/(-12)

Solve.\newline6−6x2=3x 6-6 x^{2}=3 x \newlineChoose 11 answer:\newline(A) x=3,−12 x=3,-\frac{1}{2} \newline(B) x=1±17−4 x=\frac{1 \pm \sqrt{17}}{-4} \newline(C) x=−4±343 x=\frac{-4 \pm \sqrt{34}}{3} \newline(D) x=7±193−12 x=\frac{7 \pm \sqrt{193}}{-12}

View step-by-step helpView step-by-step help
Homeright chevron icon
Math Problemsright chevron icon
Algebra 2right chevron icon
Solve a quadratic equation using the quadratic formularight chevron icon

Full solution

Q. Solve.\newline6−6x2=3x 6-6 x^{2}=3 x \newlineChoose 11 answer:\newline(A) x=3,−12 x=3,-\frac{1}{2} \newline(B) x=1±17−4 x=\frac{1 \pm \sqrt{17}}{-4} \newline(C) x=−4±343 x=\frac{-4 \pm \sqrt{34}}{3} \newline(D) x=7±193−12 x=\frac{7 \pm \sqrt{193}}{-12}
  1. Rearrange Equation: First, we need to rearrange the equation into the standard quadratic form ax2+bx+c=0ax^2 + bx + c = 0.\newline6−6x2=3x6 - 6x^2 = 3x\newlineMove all terms to one side of the equation to get zero on the other side.\newline−6x2−3x+6=0-6x^2 - 3x + 6 = 0\newlineNow, we have a quadratic equation in the form ax2+bx+c=0ax^2 + bx + c = 0, where a=−6a = -6, b=−3b = -3, and c=6c = 6.
  2. Quadratic Formula: Next, we will use the quadratic formula to find the solutions for xx. The quadratic formula is x=−b±b2−4ac2ax = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Here, a=−6a = -6, b=−3b = -3, and c=6c = 6.
  3. Calculate Discriminant: Now, we calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac.\newlineDiscriminant = (−3)2−4(−6)(6)(-3)^2 - 4(-6)(6)\newlineDiscriminant = 9−(−144)9 - (-144)\newlineDiscriminant = 9+1449 + 144\newlineDiscriminant = 153153
  4. Plug Values into Formula: With the discriminant calculated, we can now plug the values into the quadratic formula.\newlinex=−(−3)±1532(−6)x = \frac{-(-3) \pm \sqrt{153}}{2(-6)}\newlinex=3±153−12x = \frac{3 \pm \sqrt{153}}{-12}
  5. Simplify Square Root: We simplify the square root of 153153 to get the exact solutions.\newline153\sqrt{153} is not a perfect square, so we leave it as is.\newlinex=3±153−12x = \frac{3 \pm \sqrt{153}}{-12}
  6. Compare Solutions: Now we have two possible solutions for xx, which correspond to the ±\pm in the formula.x=3+153−12x = \frac{3 + \sqrt{153}}{-12} or x=3−153−12x = \frac{3 - \sqrt{153}}{-12}These are the exact solutions in simplified radical form.
  7. Compare Solutions: Now we have two possible solutions for xx, which correspond to the ＂±＂ in the formula.x=(3+153)(−12)x = \frac{(3 + \sqrt{153})}{(-12)} or x=(3−153)(−12)x = \frac{(3 - \sqrt{153})}{(-12)}These are the exact solutions in simplified radical form.We can now compare our solutions to the answer choices given.(A)x=3,−(12)(A) x = 3, -(\frac{1}{2}) - This does not match our solutions.(B)x=(1±17)(−4)(B) x = \frac{(1 ± \sqrt{17})}{(-4)} - This does not match our solutions.(C)x=(−4±34)(3)(C) x = \frac{(-4 ± \sqrt{34})}{(3)} - This does not match our solutions.(D)x=(7±193)(−12)(D) x = \frac{(7 ± \sqrt{193})}{(-12)} - This does not match our solutions.Our solutions do not match any of the given answer choices exactly, which suggests there may be a mistake in the answer choices or in our calculations.

More problems from Solve a quadratic equation using the quadratic formula

Question
Solve by completing the square.\newlinem2−10m−29=0m^2 - 10m - 29 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newline`m` = ____ or `m` = _____
Get tutor helpright-arrow

Posted 8 months ago

Question
Find g(x) g(x) , where g(x) g(x) is the translation 5 5 units up of f(x)=x2 f(x)=x^2 .\newlineWrite your answer in the form a(x–h)2+k a(x–h)^2+k , where a a , h h , and k k are integers.\newlineg(x)= g(x)= ____
Get tutor helpright-arrow

Posted 7 months ago

Question
What is the range of this quadratic function?\newliney=x2−4x+4y = x^2 - 4x + 4\newlineChoices:\newline{y∣y≥2}\left\{y \mid y \geq 2\right\}\newline{y∣y≤0}\left\{y \mid y \leq 0\right\}\newline{y∣y≥0}\left\{y \mid y \geq 0\right\}\newlineall real numbers\text{all real numbers}
Get tutor helpright-arrow

Posted 5 months ago

Question
Write the equation of the parabola that passes through the points (1,0)(1,0), (2,0)(2,0), and (3,–16)(3,\text{–}16). Write your answer in the form y=a(x–p)(x–q)y = a(x – p)(x – q), where aa, pp, and qq are integers, decimals, or simplified fractions.\newline______
Get tutor helpright-arrow

Posted 5 months ago

Question
Complete the square. Fill in the number that makes the polynomial a perfect-square quadratic.\newlinef2+8f+_____f^2 + 8f + \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Solve for h h .\newlineh2+39h=0 h^2 + 39h = 0 \newline\newlineWrite each solution as an integer, proper fraction, or improper fraction in simplest form. If there are multiple solutions, separate them with commas.\newlineh= h = ____\newline
Get tutor helpright-arrow

Posted 5 months ago

Question
Write a quadratic function with zeros −9-9 and −7-7.\newlineWrite your answer using the variable xx and in standard form with a leading coefficient of 11.\newlinef(x)=_____f(x) = \_\_\_\_\_
Get tutor helpright-arrow

Posted 5 months ago

Question
Find the equation of the axis of symmetry for the parabola y=x2y = x^2. \newlineSimplify any numbers and write them as proper fractions, improper fractions, or integers.\newline‾\underline{\hspace{3cm}}
Get tutor helpright-arrow

Posted 4 months ago

Question
Find g(x)g(x), where g(x)g(x) is the translation 88 units up of f(x)=x2f(x) = x^2.\newlineWrite your answer in the form a(x–h)2+ka(x – h)^2 + k, where aa, hh, and kk are integers.\newlineg(x)=g(x) = ______\newline
Get tutor helpright-arrow

Posted 4 months ago

Question
Solve for xx.\newlinex2=1x^2 = 1\newline\newlineWrite your answer in simplified, rationalized form.\newlinex=x = ______ or x=x = ______\newline
Get tutor helpright-arrow

Posted 5 months ago

View all (109)

Related topics

Algebra - Order of OperationsAlgebra - Distributive Property`X` and `Y` AxesGeometry - Scalene TriangleCommon MultipleGeometry - Quadrant