Question

Determine the roots of the following equation. Show your work. x^2 +4x = 12

Answer 1

The root of the equation is 2 and -6

Explanation:

Given the quadratic equation x^2 + 4x = 12

Equating the equation to zero, we will have

x^2 + 4x - 12 = 0

The above quadratic function can be solved using the factorization method

Step 1: find the factors of -12 that will give +4 when add and -12 when multiply

The only factor is -2 and 6

x^2 -2x + 6x - 12 = 0

x(x - 2) + 6 (x - 2) = 0

(x - 2) (x + 6) = 0

(x - 2) = 0 or (x + 6) = 0

x - 2 = 0 or x + 6 = 0

x = 0 + 2 or x = 0- 6

x = 2 or x = -6

Hence, the root of the equation is 2 and -6

`\begin{gathered} \text{ Using the general formula} \\ x\text{ = }\frac{(-b)\text{ }\pm\sqrt[]{b^2\text{ - 4ac}}}{2a} \\ \text{The standard quadratic equation is written as} \\ ax^2\text{ + bx + c = 0} \\ \text{Given the equation; x}^2\text{ + 4x - 12} \\ \text{let a = 1, b = 4 and c = -12} \\ x\text{ = }\frac{-4\text{ }\pm\sqrt[]{4^2\text{ - 4(1}\cdot\text{ -12)}}}{2\cdot\text{ 1}} \\ x\text{ = }\frac{-4\text{ }\pm\sqrt[]{16\text{ + 48}}}{2} \\ x\text{ = }\frac{-4\pm\sqrt[]{64}}{2} \\ x\text{ = }(-4\pm8)/(2) \\ \\ x\text{ = }\frac{-4\text{ + 8}}{2}\text{ or }\frac{-4\text{ - 8}}{2} \\ x\text{ = }(4)/(2)\text{ or }(-12)/(2) \\ x\text{ = 2 or -6} \\ \text{Hence, the root of the equation is 2 and -6} \end{gathered}`