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McGraw Hill Integrated II, 2012
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McGraw Hill Integrated II, 2012 View details
Study Guide and Review
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Exercise 50 Page 83

Make sure you rewrite the equation leaving all the terms on one side and that you factor out the greatest common factor if it exists.

5, - 10

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

x^2+5x-50=0
WriteDiff

Write as a difference

x^2+10x-5x-50=0
â–¼
Factor out x & - 5
FactorOut

Factor out x

x(x+10)-5x-50=0
FactorOut

Factor out - 5

x(x+10)-5(x+10)=0
FactorOut

Factor out (x+10)

(x-5)(x+10)=0

Solving

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

(x-5)(x+10)=0
ZeroProdProp

Use the Zero Product Property

lcx-5=0 & (I) x+10=0 & (II)
AddEqn

(I): LHS+5=RHS+5

lx=5 x+10=0
SubEqn

(II): LHS-10=RHS-10

lx_1=5 x_2=- 10

Checking Our Answer

 Checking our answer
We can substitute our solutions back into the given equation and simplify to check if our answers are correct. We will start with x=5.

x^2+5x-50=0
Substitute

x= 5

5^2+5( 5)-50? =0
â–¼
Simplify
CalcPow

Calculate power

25+5(5)-50? =0
Multiply

Multiply

25+25-50? =0
AddSubTerms

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=5 is a solution of the equation. Let's move on to x=- 10.

x^2+5x-50=0
Substitute

x= - 10

( - 10)^2+5( - 10)-50? =0
â–¼
Simplify
CalcPow

Calculate power

100+5(-10)-50? =0
MultPosNeg

a(- b)=- a * b

100-50-50? =0
SubTerms

Subtract terms

0=0 ✓

Again, we created a true statement. x=- 10 is indeed a solution of the equation.

Subchapter links expand_more
arrow_right 1 Adding and Subtracting Polynomials p.81
11
Adding and Subtracting Polynomials 12 (Page 81)
Adding and Subtracting Polynomials 13 (Page 81)
Adding and Subtracting Polynomials 14 (Page 81)
Adding and Subtracting Polynomials 15 (Page 81)
Adding and Subtracting Polynomials 16 (Page 81)
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Adding and Subtracting Polynomials 18 (Page 81)
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Multiplying a Polynomial by a Monomial 19 (Page 81)
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arrow_right 3 Multiplying Polynomials p.81
Multiplying Polynomials 23 (Page 81)
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arrow_right 4 Special Products p.82
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arrow_right 5 Using the Distributive Property p.82
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arrow_right 6 Solving x^2+bx+c=0 p.83
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arrow_right 7 Solving ax^2+bx+c=0 p.83
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