4. Solving Quadratic Equations by Completing the Square
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Substitute the information given into the rectangle area formula, then simplify.
Length: 18 ft.
Width: 8 ft.
When we are given the area of a rectangle, we generally need to use the formula for the area of a rectangle. In this case we need to write expressions for the length, ℓ, and width, w.
Verbal Expression | Algebraic Expression |
---|---|
the length is 10 ft more than the width | ℓ=10+w |
A=144, ℓ=10+w
Distribute w
LHS−144=RHS−144
Commutative Property of Addition
Rearrange equation
Factors | Sum of factors |
---|---|
-1,144 | 143 |
-2,72 | 70 |
-3,48 | 45 |
-4,36 | 32 |
-6,24 | 18 |
-8,18 | 10 |
Use the Zero Product Property
(I): LHS+8=RHS+8
(II): LHS−18=RHS−18