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Chapter 0: Problem 76

Solve each quadratic equation using the quadratic formula. $$x^{2}+8 x+12=0$$

Short Answer

Expert verified
The solutions of the equation \(x^{2}+8 x+12=0\) are \(x = -2\) and \(x = -6\).

Step by step solution

01

- Identify the coefficients

In the given quadratic equation \(x^{2}+8 x+12=0\), here \(a=1\), \(b=8\) and \(c=12\).
02

- Implement Quadratic Formula

The quadratic formula is given by \[x=\frac{-b \pm \sqrt {b^2 -4ac}}{2a}\]. By substituting the values of a, b and c from our equation into the formula, it is obtained that \(x=\frac{-8 \pm \sqrt {(8)^2 -4(1)(12)}}{2(1)}\)
03

- Simplify the Expression

Solving further, we get \[x=\frac{-8 \pm \sqrt {64 -48}}{2}= \frac{-8 \pm \sqrt {16}}{2}\]. This simplifies to \[x= \frac{-8 \pm 4}{2}.\]
04

- Find the Roots

Upon solving the equation, two roots are obtained: \(x= \frac{-8+4}{2} =-2\) and \(x= \frac{-8-4}{2}= -6\). Therefore, the solutions of the given quadratic equation are \(x = -2\) and \(x = -6\).

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