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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 27 Page 49

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

- 4, - 14

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.

d^2+56=- 18d

LHS+18d=RHS+18d

d^2+18d+56=0

Write as a sum

d^2+4d+14d+56=0

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Factor out d & 14

Factor out d

d(d+4)+14d+56=0

Factor out 14

d(d+4)+14(d+4)=0

Factor out (d+4)

(d+4)(d+14)=0

Solving

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

(d+4)(d+14)=0

Use the Zero Product Property

lcd+4=0 & (I) d+14=0 & (II)

(I): LHS-4=RHS-4

ld=- 4 d+14=0

(II): LHS-14=RHS-14

ld_1=- 4 d_2=- 14

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 d=- 4.

d^2+56=- 18d

d= - 4

( -4)^2+56? =- 18( -4)

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Simplify

Calculate power

16+56? =- 18(- 4)

MultNegNegOnePar

- a(- b)=a* b

16+56? =72

Add terms

72=72 ✓

Substituting and simplifying created a true statement, so we know that d=- 4 is a solution of the equation. Let's move on to d=- 14.

d^2+56=- 18d

d= - 14

( -14)^2+56? =- 18( - 14)

▼

Simplify

Calculate power

196+56? =- 18(- 14)

MultNegNegOnePar

- a(- b)=a* b

196+56? =252

Add terms

252=252 ✓

Again, we created a true statement. d=- 14 is indeed a solution of the equation.

Subchapter links

Exercises p.49-51