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Chapter 5: Problem 20

Solve. SEE EXAMPLE 1. (OBJECTIVE 1) $$x^{2}+x-20=0$$

Short Answer

Expert verified
The solutions to the given quadratic equation \(x^{2}+x-20=0\) are x=-5 and x=4.

Step by step solution

01

Identifying the Form of Quadratic Equation

The provided equation \(x^{2}+x-20=0\) is in the form of a quadratic equation i.e., \(ax^{2}+bx+c=0\). In this case, a = 1, b = 1 and c = -20.
02

Factoring the Quadratic Expression

The quadratic expression can be factored by searching for two numbers which add up to b and multiply to ac. In our case, b=1 and ac=(-1*20)=-20. The numbers are 5 and -4, because 5*(-4)=-20 and 5+(-4)=1. With these two numbers, the given quadratic equation factors into \((x+5)(x-4)=0\).
03

Solving for x

Now having the factors \((x+5)(x-4)=0\), the values for x can be found by setting each factor equal to zero and solving each resulting equation. So we get two equations: x+5=0 and x-4=0. Solving these gives us x=-5 and x=4.

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Key Concepts

These are the key concepts you need to understand to accurately answer the question.

Factoring Quadratics
Factoring quadratic equations is a critical skill in algebra because it's one of the more direct methods for finding the roots of a polynomial.

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Most popular questions from this chapter

Factor. $$8 r^{2}-10 r s-25 s^{2}$$

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