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Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698

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BuyFindarrow_forward

Elementary Geometry for College St...

6th Edition
Daniel C. Alexander + 1 other
ISBN: 9781285195698
Textbook Problem
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Find the length a by solving the equation a 2 + a + 1 2 = 25

Chapter A.4, Problem 39E, Find the length a by solving the equation a2+a+12=25

To determine

The length ‘a’ by solving the equation a2+a+12=25.

Explanation

Approach:

Solving an equation is to find the value of the unknown variables in the equation, such that the obtained value or values of the unknown should satisfy the equation from which it was derived. Such a value is said to be the solution for the equation. In general a quadratic equation has two solutions for the variable in the equation as the degree of the equation is two.

Calculation:

Given,

a2+a+12=25

Apply the identity a+b2=a2+2ab+b2 for to expand a+12.

a2+a2+2a1+12=25

a2+a2+2a+1=25

Add; -25 on both sides,

a2+a2+2a+1+-25=25+-25

Combine; the like terms.

a2+a2+2a+1-25=25-25

2a2+2a+-24=0

Divide; each term of the above equation by 2 on both sides,

2a22+2a2+-242=02

a2+a-12=0

The above equation is in the standard form of a quadratic equation.

Now, we shall proceed with the factorization of the quadratic expression in the left of the equation.

First look for the common factor GCF of the terms a2, a and -12

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