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.\newline3g2−8g+4=03g^2 - 8g + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____

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

Full solution

Q. Solve using the quadratic formula.\newline3g2−8g+4=03g^2 - 8g + 4 = 0\newlineWrite your answers as integers, proper or improper fractions in simplest form, or decimals rounded to the nearest hundredth.\newlineg=g = _____ or g=g = _____
  1. Quadratic Formula Definition: The quadratic formula is given by g=−b±b2−4ac2ag = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}, where aa, bb, and cc are the coefficients of the quadratic equation ax2+bx+c=0ax^2 + bx + c = 0. For the equation 3g2−8g+4=03g^2 - 8g + 4 = 0, a=3a = 3, b=−8b = -8, and c=4c = 4.
  2. Calculate Discriminant: First, calculate the discriminant, which is the part under the square root in the quadratic formula: b2−4acb^2 - 4ac. Here, it is (−8)2−4(3)(4)(-8)^2 - 4(3)(4).
  3. Discriminant Calculation: Perform the calculation: (−8)2−4(3)(4)=64−48=16(-8)^2 - 4(3)(4) = 64 - 48 = 16.
  4. Apply Quadratic Formula: Now, apply the quadratic formula with the calculated discriminant. The solutions for gg will be g=−(−8)±162×3g = \frac{-(-8) \pm \sqrt{16}}{2 \times 3}.
  5. Simplify Equation: Simplify the equation: g=8±166g = \frac{8 \pm \sqrt{16}}{6}.
  6. Solve for Solutions: Since 16=4\sqrt{16} = 4, the equation becomes g=(8±4)6g = \frac{(8 \pm 4)}{6}.
  7. Calculate Solutions: Now, solve for the two possible values of gg: g=8+46g = \frac{8 + 4}{6} and g=8−46g = \frac{8 - 4}{6}.
  8. Simplify Fractions: Calculate the two solutions: g=126g = \frac{12}{6} and g=46.g = \frac{4}{6}.
  9. Simplify Fractions: Calculate the two solutions: g=126g = \frac{12}{6} and g=46g = \frac{4}{6}.Simplify the fractions: g=2g = 2 and g=23g = \frac{2}{3}.

More problems from Solve a quadratic equation using the quadratic formula

Question
The function h(t)=−16t2+144h(t) = -16t^{2} + 144 represents the height, h(t)h(t), in feet, of an object from the ground at tt seconds after it is dropped. A realistic domain (for time) for this function is:\newline(A)(A) −3≤t≤3-3 \leq t \leq 3\newline(B)(B) 0≤t≤30 \leq t \leq 3\newline(C)(C) 0≤h≤1440 \leq h \leq 144\newline(D)(D) all real numbers
Get tutor helpright-arrow

Posted 8 months ago

Question
Деление с остатком
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=x2+40x−20y = x^2 + 40x - 20\newliney=40x−4y = 40x - 4\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=−36x+26y = -36x + 26\newliney=x2−46x−13y = x^2 - 46x - 13\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=32x2+32x−23y = 32x^2 + 32x - 23\newliney=32x+9y = 32x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=x2+12x−41y = x^2 + 12x - 41\newliney=17x+9y = 17x + 9\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=x2−43x−14y = x^2 - 43x - 14\newliney=−45x+34y = -45x + 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Solve the system of equations.\newliney=14x−26y = 14x - 26\newliney=2x2+14x−34y = 2x^2 + 14x - 34\newlineWrite the coordinates in exact form. Simplify all fractions and radicals.\newline(______,______)\newline(______,______)
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the discriminant.\newline3u2−8u+4=03u^2 - 8u + 4 = 0
Get tutor helpright-arrow

Posted 8 months ago

Question
Find the discriminant.\newline7w2+5w+8=07w^2 + 5w + 8 = 0
Get tutor helpright-arrow

Posted 8 months ago

View all (21)

Related topics

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