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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

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Exercise 10 Page 188

Rewrite the x-term as a sum of two x-terms. Recall the Zero Product Property.

x=- 3 and x=4

We want to solve the given equation by factoring.

Factoring

Let's start by rewriting - x as the sum of - 4x and 3x. Then we can factor the equation.

x^2-x-12=0

Write as a sum

x^2-4x+3x-12=0

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Factor out x & 3

Factor out x

x(x-4)+3x-12=0

Factor out 3

x(x-4)+3(x-4)=0

Factor out (x-4)

(x+3)(x-4)=0

Solving

To solve this equation, we will apply the Zero Product Property.

(x+3)(x-4)=0

Use the Zero Product Property

lcx+3=0 & (I) x-4=0 & (II)

(I): LHS-3=RHS-3

lx=- 3 x-4=0

(II): LHS+4=RHS+4

lx_1=- 3 x_2=4

We have found that the equation has two solutions, - 3 and 4.

Checking Our Answer

Checking Our Answer

We can check our solutions by substituting them in the given equation and simplifying. If the equation produces a true statement, our solution is correct. Let's start with x=- 3.

x^2-x-12=0

x= - 3

( -3)^2-( -3)-12? =0

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Simplify

Calculate power

9-(-3)-12? =0

a-(- b)=a+b

9+3-12? =0

Add and subtract terms

0=0 ✓

Since the equation produced a true statement, x=- 3 is a correct solution. Let's now check x=4.

x^2-x-12=0

x= 4

( 4)^2-( 4)-12? =0

▼

Simplify

Calculate power

16-4-12? =0

Subtract terms

0=0 ✓

Again, the substitution produced a true statement. Therefore, x=4 is also a correct solution.