**Solving a Quadratic Equation**In this example, we are given a quadratic equation:\[ 6x^2 - 8 = 36x \]To solve this quadratic equation, we need to follow these steps:1. **Rewrite the equation in standard form.** The standard form of a quadratic equation is \( ax^2 + bx + c = 0 \). First, let's move all the terms to one side of the equation: \[ 6x^2 - 8 - 36x = 0 \] Rearrange the terms to match the standard form: \[ 6x^2 - 36x - 8 = 0 \]2. **Identify the coefficients \(a\), \(b\), and \(c\)** from the standard form: \[ a = 6 \] \[ b = -36 \] \[ c = -8 \]3. **Solve the quadratic equation.** There are multiple methods to solve a quadratic equation, such as factoring, completing the square, or using the quadratic formula. Let's use the quadratic formula here: \[ x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{2a} \] Plug in the values of \(a\), \(b\), and \(c\): \[ x = \frac{{-(-36) \pm \sqrt{{(-36)^2 - 4(6)(-8)}}}}{2(6)} \] \[ x = \frac{{36 \pm \sqrt{{1296 + 192}}}}{12} \] \[ x = \frac{{36 \pm \sqrt{{1488}}}}{12} \] \[ x = \frac{{36 \pm 38.6}}{12} \] This yields two potential solutions: \[ x = \frac{{36 + 38.6}}{12} = \frac{{74.6}}{12} \approx 6.217 \] \[ x = \frac{{36 - 38.6}}{12} = \frac{{-2.6}}{12} \approx -0.217 \]Therefore, the solutions to the equation \( 6x^2 - 8 = 36x \) are approximately:

Name: **Solving a Quadratic Equation**In this example, we are given a quadr
Uploaded: 2024-03-20T07:06:41.000Z
Channel: Bartleby
Description: **Solving a Quadratic Equation**In this example, we are given a quadratic equation:\[ 6x^2 - 8 = 36x \]To solve this quadratic equation, we need to follow these steps:1. **Rewrite the equation in standard form.** The standard form of a quadratic equ