/*! This file is auto-generated */ .wp-block-button__link{color:#fff;background-color:#32373c;border-radius:9999px;box-shadow:none;text-decoration:none;padding:calc(.667em + 2px) calc(1.333em + 2px);font-size:1.125em}.wp-block-file__button{background:#32373c;color:#fff;text-decoration:none} Problem 53 Solve the equations in Exercises... [FREE SOLUTION] | 91影视

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Chapter 6: Problem 53

Solve the equations in Exercises 53-72 using the quadratic formula. \(x^{2}+8 x+15=0\)

Short Answer

Expert verified
The solutions for the equation \(x^{2}+8x+15 = 0\) are \(x_{1} = -3\) and \(x_{2} = -5\).

Step by step solution

01

Identifying coefficients

In the equation \(x^{2}+8x+15 = 0\), the coefficients are \(a=1, b=8, c=15\). These values will be used in the quadratic formula.
02

Calculating the determinant

The determinant is part of the quadratic formula and is calculated as \(b^{2} - 4ac = (8)^{2} - 4*1*15 = 4\). This value is greater than 0, so the quadratic equation has two real solutions.
03

Applying the Quadratic formula

Insert the known values \(a=1, b=8, c=15\) into the quadratic formula. We get \(x = \frac{-8 \pm \sqrt{4}}{2*1}\). This means \(x = -8 \pm 2\)/2.
04

Solving for x

Continuing with the computation gives two x solutions: \( x_{1} = (-8 + 2)/2 = -3, x_{2} = (-8 - 2)/2 = -5 \).

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