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McGraw Hill Integrated II, 2012 View details

Mid-Chapter Quiz

Finish the assignment

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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

WriteSum

Write as a sum

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

▼

Factor out x & 3

FactorOut

Factor out x

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

FactorOut

Factor out 3

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

FactorOut

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

ZeroProdProp

Use the Zero Product Property

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

SubEqn

(I): LHS-3=RHS-3

lx=- 3 x-4=0

AddEqn

(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

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

Substitute

x= - 3

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

▼

Simplify

CalcPow

Calculate power

9-(-3)-12? =0

SubNeg

a-(- b)=a+b

9+3-12? =0