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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 26 Page 49

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

- 8, 15

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.

n^2-120=7n

LHS-7n=RHS-7n

n^2-7n-120=0

Write as a difference

n^2+8n-15n-120=0

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Factor out n & - 15

Factor out n

n(n+8)-15n-120=0

Factor out - 15

n(n+8)-15(n+8)=0

Factor out (n+8)

(n+8)(n-15)=0

Solving

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

(n+8)(n-15)=0

Use the Zero Product Property

lcn+8=0 & (I) n-15=0 & (II)

(I): LHS-8=RHS-8

ln=- 8 n-15=0

(II): LHS+15=RHS+15

ln_1=- 8 n_2=15

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 n=- 8.

n^2-120=7n

n= - 8

( -8)^2-120? =7( - 8)

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Simplify

Calculate power

64-120? =7(- 8)

a(- b)=- a * b

64-120? =- 56

Subtract term

- 56=-56 ✓

Substituting and simplifying created a true statement, so we know that n=- 8 is a solution of the equation. Let's move on to n=15.

n^2-120=7n

n= 15

15^2-120? =7( 15)

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Simplify

Calculate power

225-120? =7(15)

Multiply

225-120? =105

Subtract term

105=105 ✓

Again, we created a true statement. n=15 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51