Question

Use the quadratic formula to solve the equation. $$2 x^{2}-2 x-12=0$$

Short answer

The solutions to the quadratic equation \(2x^2 - 2x -12 = 0\) are \(x = 3\) and \(x = -2\).

Step-by-step solution

Identify a, b, c

From the given equation, one can identify the coefficients as \(a = 2\), \(b = -2\), and \(c = -12\)

Substitute values into the quadratic equation

Substitute the values of a, b, c into the quadratic formula. Thus, \(x=\frac{-(-2)\pm\sqrt{(-2)^{2}-4*2*(-12)}}{2*2}\)

Simplify the equation

Simplify the formula will give \(x = \frac{2\pm\sqrt{4+96}}{4}\)

Find the roots

The solutions step by step will be \(x = \frac{2\pm\sqrt{100}}{4} ----> x=\frac{2\pm10}{4}\). Therefore, the roots of the equation are \(3\) and \(-2\).