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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 5 Page 49

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

- 3, 7

Practice makes perfect

We want to solve the given equation by factoring.

Factoring

Let's start factoring the expression!

x^2-4x-21=0

Write as a difference

x^2+3x-7x-21=0

▼

Factor out x & -7

Factor out x

x(x+3)-7x-21=0

Factor out - 7

x(x+3)-7(x+3)=0

Factor out (x+3)

(x+3)(x-7)=0

Solving

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

(x+3)(x-7)=0

Use the Zero Product Property

lcx+3=0 & (I) x-7=0 & (II)

(I): LHS-3=RHS-3

lx=- 3 x-7=0

(II): LHS+7=RHS+7

lx_1=- 3 x_2=7

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=- 3.

x^2-4x-21=0

x= - 3

( -3)^2-4( -3)-21? =0

▼

Simplify

Calculate power

9-4(-3)-21? =0

MultNegNegOnePar

- a(- b)=a* b

9+12-21? =0

Add and subtract terms

0=0 ✓

Substituting and simplifying created a true statement, so we know that x=- 3 is a solution of the equation. Let's move on to x=7.

x^2-4x-21=0

x= 7

7^2-4( 7)-21? =0

▼

Simplify

Calculate power

49-4(7)-21? =0

Multiply

49-28-21? =0

Subtract terms

0=0 ✓

Again, we created a true statement. x=7 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51