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Chapter 0: Problem 75

Solve each quadratic equation using the quadratic formula. $$x^{2}+8 x+15=0$$

Short Answer

Expert verified
The solutions of the equation are \(x = -3\) and \(x = -5\).

Step by step solution

01

Identify the Coefficients

The quadratic equation is in the form \(ax^{2} + bx + c = 0\). From the equation \(x^{2}+8x+15=0\), we can identify \(a=1, b=8\) and \(c=15\).
02

Apply the Quadratic Formula

The quadratic formula is \(x = \frac{-b \pm \sqrt {b^{2}-4ac}}{2a}\). Substituting the identified coefficients we get \(x = \frac{-8 \pm \sqrt {8^{2}-4*1*15}}{2*1}\).
03

Simplify the Expression

This simplifies to \(x = \frac{-8 \pm \sqrt {64-60}}{2}\) which further simplifies to \(x = \frac{-8 \pm \sqrt {4}}{2}\). So the solutions are \(x = \frac{-8 + 2}{2} = -3\) and \(x = \frac{-8 - 2}{2}=-5\).

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