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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

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

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Exercise 24 Page 49

Start by factoring the equation. Then, use the Zero Product Property to solve it.

- 1, - 9

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

c^2+10c+9=0

Write as a sum

c^2+c+9c+9=0

▼

Factor out c & 9

Factor out c

c(c+1)+9c+9=0

Factor out 9

c(c+1)+9(c+1)=0

Factor out (c+1)

(c+1)(c+9)=0

Solving

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

(c+1)(c+9)=0

Use the Zero Product Property

lcc+1=0 & (I) c+9=0 & (II)

(I): LHS-1=RHS-1

lc=- 1 c+9=0

(II): LHS-9=RHS-9

lc_1=- 1 c_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 c=- 1.

c^2+10c+9=0

c= - 1

( -1)^2+10( -1)+9? =0

▼

Simplify

Calculate power

1+10(-1)+9? =0

a(- b)=- a * b

1-10+9? =0

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that c=- 1 is a solution of the equation. Let's move on to c=- 9.

c^2+10c+9=0

c= - 9

( -9)^2+10( -9)+9? =0

▼

Simplify

Calculate power

81+10(-9)+9? =0

a(- b)=- a * b

81-90+9? =0

Add and subtract terms

0=0 ✓

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

Subchapter links

Exercises p.49-51