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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 8 Page 49

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

- 8, - 4

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.

x^2+12x=- 32

LHS+32=RHS+32

x^2+12x+32=0

Write as a sum

x^2+8x+4x+32=0

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Factor out x & 4

Factor out x

x(x+8)+4x+32=0

Factor out 4

x(x+8)+4(x+8)=0

Factor out (x+8)

(x+8)(x+4)=0

Solving

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

(x+8)(x+4)=0

Use the Zero Product Property

lcx+8=0 & (I) x+4=0 & (II)

(I): LHS-8=RHS-8

lx=- 8 x+4=0

(II): LHS-4=RHS-4

lx_1=- 8 x_2=- 4

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=- 8.

x^2+12x=- 32

x= - 8

( -8)^2+12( -8)? =- 32

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Simplify

Calculate power

64+12(-8)? =- 32

a(- b)=- a * b

64-96? =- 32

Subtract term

- 32=-32 ✓

Substituting and simplifying created a true statement, so we know that x=- 8 is a solution of the equation. Let's move on to x=- 4.

x^2+12x=- 32

x= - 4

( -4)^2+12( -4)? =- 32

▼

Simplify

Calculate power

16+12(-4)? =- 32

a(- b)=- a * b

16-48? =- 32

Subtract term

- 32=-32 ✓

Again, we created a true statement. x=- 4 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51