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McGraw Hill Integrated II, 2012

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McGraw Hill Integrated II, 2012 View details

6. Solving x^2+bx+c=0

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Exercise 23 Page 49

Make sure you rewrite the equation leaving all the terms on one side. Then, solve by factoring.

- 2, - 9

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start by writing all the terms on one side of the equals sign.

a^2+11a=- 18

LHS+18=RHS+18

a^2+11a+18=0

Write as a sum

a^2+2a+9a+18=0

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Factor out a & 9

Factor out a

a(a+2)+9a+18=0

Factor out 9

a(a+2)+9(a+2)=0

Factor out (a+2)

(a+2)(a+9)=0

Solving

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

(a+2)(a+9)=0

Use the Zero Product Property

lca+2=0 & (I) a+9=0 & (II)

(I): LHS-2=RHS-2

la=- 2 a+9=0

(II): LHS-9=RHS-9

la_1=- 2 a_2=- 9

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 a=- 2.

a^2+11a=- 18

a= - 2

( -2)^2+11( -2)? =- 18

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Simplify

Calculate power

4+11(-2)? =- 18

a(- b)=- a * b

4-22? =- 18

Subtract term

- 18=- 18 ✓

Substituting and simplifying created a true statement, so we know that a=- 2 is a solution of the equation. Let's move on to a=- 9.

a^2+11a=- 18

a= - 9

( -9)^2+11( -9)? =- 18

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Simplify

Calculate power

81+11(-9)? =- 18

a(- b)=- a * b

81-99? =- 18

Subtract term

- 18=- 18 ✓

Again, we created a true statement. a=- 9 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51