Completing the Square
Solve by completing the square. You must show enough work that it is clear that you used completing the square.
x^2-14x+24=0
{2, 12}
Find a negative integer with the following property: when the product of one more than three times the number with two less than the number is found it is equal to 43 more than the number.
Write an equation and solve.
x^2-2x-15=0
-3
(reject 5 as not negative)
Solve algebraically. You must show enough work that it is clear your solution is algebraic.
y=x^2-8x+15
y=x+1
{(2,3), (7,8)}
Solve by completing the square. You must show enough work that it is clear that you used completing the square.
x^2-11x+26=5x-2
{2, 14}
Three consecutive, odd, positive integers have the property that the product of the smaller two is 3 more than four times the sum of the larger two. Algebraically determine the three integers.
Write an equation and solve.
x^2-6x-27=0
9, 11, and 13
Solve algebraically. You must show enough work that it is clear your solution is algebraic.
y=x^2-12x+7
y=-8x+7
{(0,7), (4,-25)}
Solve by completing the square. You must show enough work that it is clear that you used completing the square.
5x^2+50x+80=0
{-2,-8}
A rectangle has a perimeter of 44 feet and an area of 112 feet. Find the dimensions.
Write an equation or system and solve.
x2-22x+112=0
8 x 14
Solve algebraically. You must show enough work that it is clear your solution is algebraic.
y=x^2+12x-13
y=10x+2
{(-5,-48), (3,32)}
Solve by completing the square. You must show enough work that it is clear that you used completing the square.
x^2+3x+3=8x-3
{2,3}
A square shaped stone patio is extended on one side by 6 feet and on the other side by 10 feet. The total area of patio, including the original section, is now 525 square feet.
Let x be one side of the original square.
Set up an equation and solve for one side.
x = 15 ft
Solve algebraically. You must show enough work that it is clear your solution is algebraic.
y=x^2-2x-14
y=3x+10
{(8,34), (-3,1)}
Solve by completing the square. You must show enough work that it is clear that you used completing the square.
5x^2+15x=90
{3,6}
A rectangular painting has a length that is ten inches more than the width. The painting is in a frame that is two inches wide all the way around. The total area of the picture and the frame is 336 inch squared. What are the dimensions of the painting?
10 x 20 inches
Solve algebraically. You must show enough work that it is clear your solution is algebraic.
y=x^2-22x+300
y=10x+60
{(12,180),(20,260)}