Page 716 - Algebra 1

b. 3x2 -12x=-54 SOLUTION
3x2 - 12x = -54 3x2 - 12x = -54
__ 3 3
Divide both sides by the coefficient of x2.
Simplify.
Completethesquare.Addthemissing value to both sides of the equation.
Simplify.
Factor the left side. Simplify the right side.
Take the square root of both sides of the equation.
S i m p l i f y .
Ø; No real number is the square root of a negative value.
x2 - 4x = -18 _-4 2
_-4 2 x2 -4x+(2 )=-18+(2 )
x2 -4x+4=-18+4 (x - 2)2 = -14
√ √(x - 2)2 = ± -14
x - 2 = ± √ - 1 4
x = 2 ± √- 1 4
Reading Math
A symbol for no solution is Ø.
Finding Dimensions of a Rectangle
The length of a rectangle is 12 feet more than its width. The total area of the rectangle is 64 square feet. What are the dimensions of the rectangle?
SOLUTION
Write and solve an equation to find the dimensions.
Example
4
x = width; x + 12 = length w · l = A
x(x + 12) = 64 x2 + 12x = 64
_12 2
x2 +12x+(2 )=64+(2 )
x2 +12x+36=64+36 (x + 6)2 = 100
√ √(x + 6)2 = ± 100
x + 6 = ±10 x+6=-10 or x+6=10
Assign values for the length and width. Use the area formula.
Substitute the width, length, and area. Distribute.
_12 2
Completethesquare.Addthemissing value to both sides.
Simplify.
Factor and simplify.
Take the square root of both sides. Simplify.
Writeastwoequations.
Subtract 6 from both sides.
Math Reasoning
Verify Show that w =
4 feet and l = 16 feet are the correct dimensions.
x = -16 or x = 4
A negative length is not possible, so 4 feet is the solution. This means that
the width of the rectangle is 4 feet and the length is 4 + 12, or 16 feet.
Lesson 104 701