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 using the quadratic formula.\newline7y2+7y−7=07y^2 + 7y - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____

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 using the quadratic formula.\newline7y2+7y−7=07y^2 + 7y - 7 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newliney=y = _____ or y=y = _____
  1. Identify values of aa, bb, cc: Identify the values of aa, bb, and cc in the quadratic equation 7y2+7y−7=07y^2 + 7y - 7 = 0. The quadratic equation is in the form ay2+by+c=0ay^2 + by + c = 0. Comparing this with our equation, we get: a=7a = 7 b=7b = 7 bb00
  2. Substitute into quadratic formula: Substitute the values of aa, bb, and cc into the quadratic formula y=−b±b2−4ac2ay = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}. Substitute a=7a = 7, b=7b = 7, and c=−7c = -7 into the formula. y=−(7)±(7)2−4⋅7⋅(−7)2⋅7y = \frac{-(7) \pm \sqrt{(7)^2 - 4\cdot7\cdot(-7)}}{2\cdot7}
  3. Simplify expression and calculate discriminant: Simplify the expression under the square root and calculate the discriminant.\newline(7)2−4⋅7⋅(−7)\sqrt{(7)^2 - 4\cdot7\cdot(-7)}\newline= 49+196\sqrt{49 + 196}\newline= 245\sqrt{245}
  4. Insert discriminant into formula: Insert the value of the discriminant back into the quadratic formula.\newliney=−7±2452⋅7y = \frac{-7 \pm \sqrt{245}}{2\cdot7}\newliney=−7±24514y = \frac{-7 \pm \sqrt{245}}{14}
  5. Calculate possible solutions for y: Calculate the two possible solutions for y.\newliney=−7+24514y = \frac{-7 + \sqrt{245}}{14} or y=−7−24514y = \frac{-7 - \sqrt{245}}{14}
  6. Simplify square root of 245245: Simplify the square root of 245245 to its simplest radical form if possible. 245\sqrt{245} can be simplified to 49×5\sqrt{49\times 5} which is 7×57\times\sqrt{5}. So, y=−7+7×514y = \frac{-7 + 7\times\sqrt{5}}{14} or y=−7−7×514y = \frac{-7 - 7\times\sqrt{5}}{14}
  7. Simplify fractions: Simplify the fractions.\newliney=7(−1+5)14y = \frac{7(-1 + \sqrt{5})}{14} or y=7(−1−5)14y = \frac{7(-1 - \sqrt{5})}{14}\newliney=−1+52y = \frac{-1 + \sqrt{5}}{2} or y=−1−52y = \frac{-1 - \sqrt{5}}{2}
  8. Round values of y: If necessary, round the values of y to the nearest hundredth. \newliney≈(−1+2.24)/2y \approx (-1 + 2.24) / 2 or y≈(−1−2.24)/2y \approx (-1 - 2.24) / 2\newliney≈1.24/2y \approx 1.24 / 2 or y≈−3.24/2y \approx -3.24 / 2\newliney≈0.62y \approx 0.62 or y≈−1.62y \approx -1.62

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