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McGraw Hill Integrated II, 2012

MH

McGraw Hill Integrated II, 2012 View details

1. Solving Quadratic Equations by Factoring

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Exercise 40 Page 174

Use the formula for the difference of two squares.

11 and -11

Practice makes perfect

We want to solve the given equation by factoring.

Rewriting the Equation

To do so, we will first rewrite the equation to have everything on one side of the equals sign. x^2=121 ⇔ x^2-121=0

Applying the Difference of Two Squares

Do you notice that the expression on the left-hand side of the equation is a difference of two perfect squares? This can be factored using the difference of squares method. a^2 - b^2 ⇔ (a+b)(a-b) To do so, we first need to express each term as a perfect square.

Expression	x^2-121
Rewrite as Perfect Squares	x^2 - 11^2
Apply the Formula	(x+11)(x-11)

Solving the Equation

Finally, to solve the equation, we will use the Zero Product Property.

x^2-121=0

▼

a^2-b^2=(a+b)(a-b)

Write as a power

x^2-11^2=0

a^2-b^2=(a+b)(a-b)

(x+11)(x-11)=0

Use the Zero Product Property

lcx+11=0 & (I) x-11=0 & (II)

(I): LHS-11=RHS-11

lx=- 11 x-11=0

(II): LHS+11=RHS+11

lx_1=- 11 x_2=11

Subchapter links

Exercises p.174-177