Question

Quadratic Equations problem: -16x^2 = 24x + 9 using the FORMULA in the picture attached to solve.

Answer 1

Step 1: Problem

`\begin{gathered} -16x^2\text{ = 24x + 9} \\ 16x^2\text{ + 24x + 9 = 0} \end{gathered}`

Step 2: Concept

Apply the quadratic equation formula

`x\text{ = }\frac{-b\text{ }\pm\text{ }\sqrt[]{b^2\text{ - 4ac}}}{2a}`

Step 3: Method

a = 16

b = 24

c = 9

`\begin{gathered} x\text{ = }\frac{-\text{ 24 }\pm\text{ }\sqrt[]{24^2\text{ - 4 }*\text{ 16 }*\text{ 9}}}{2\text{ }*\text{ 16}} \\ x\text{ = }\frac{-\text{ 24 }\pm\text{ }\sqrt[]{576\text{ - 576}}}{32} \\ x\text{ = }\frac{\text{ - 24 }\pm\text{ }\sqrt[]{0}}{32} \\ x\text{ = }\frac{-\text{ 24 }\pm\text{ 0}}{32} \\ x\text{ = }\frac{-\text{ 24 + 0}}{32}\text{ or }\frac{-24\text{ - 0}}{32} \\ x\text{ = }(-24)/(32)\text{ or }\frac{-\text{ 24}}{32} \\ x\text{ = }(-3)/(4)\text{ twice} \end{gathered}`