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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 10 Page 49

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

4, 6

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^2-10x=- 24

LHS+24=RHS+24

x^2-10x+24=0

Write as a difference

x^2-4x-6x+24=0

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Factor out x & - 6

Factor out x

x(x-4)-6x+24=0

Factor out - 6

x(x-4)-6(x-4)=0

Factor out (x-4)

(x-4)(x-6)=0

Solving

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

(x-4)(x-6)=0

Use the Zero Product Property

lcx-4=0 & (I) x-6=0 & (II)

(I): LHS+4=RHS+4

lx=4 x-6=0

(II): LHS+6=RHS+6

lx_1=4 x_2=6

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=4.

x^2-10x=- 24

x= 4

4^2-10( 4)? =- 24

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Simplify

Calculate power

16-10(4)? =- 24

Multiply

16-40? =- 24

Subtract term

- 24=-24 ✓

Substituting and simplifying created a true statement, so we know that x=4 is a solution of the equation. Let's move on to x=6.

x^2-10x=- 24

x= 6

6^2-10( 6)? =- 24

▼

Simplify

Calculate power

36-10(6)? =- 24

Multiply

36-60? =- 24

Subtract term

- 24=-24 ✓

Again, we created a true statement. x=6 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51