Marina solved the quadratic equation 9x^2 - 36x - 720 = 0 by completing the square. In the process, she came up with the equivalent equation
(x + r)^2 = s
where r and s are constants. What is s?
+421 Divide by 9 on both sides
x^2 + 6x - 80 = 0
So x^2 + 6x = 80
(6/2)^2 = 9
s = 80 + 9 = 89
Solve for x:
9 x^2 - 36 x - 720 = 0
Divide both sides by 9:
x^2 - 4 x - 80 = 0
Add 80 to both sides:
x^2 - 4 x = 80
Add 4 to both sides:
x^2 - 4 x + 4 = 84
Write the left hand side as a square:
(x - 2)^2 = 84
Take the square root of both sides:
x - 2 = 2 sqrt(21) or x - 2 = -2 sqrt(21)
Add 2 to both sides:
x = 2 + 2 sqrt(21) or x - 2 = -2 sqrt(21)
Add 2 to both sides:
x = 2 + 2 sqrt(21) or x = 2 - 2 sqrt(21)
[ (2+2sqrt(21)) + (2 - 2sqrt(21))]^2 ==4^2 ==16
+128399 Factor out the 9
9 (x^2 - 4x - 80) = 0
Take 1/2 of 4 = 2...square it = 4.....add and subtract it within the parentheses
9 ( x^2 - 4x + 4 - 80 - 4) factor the first three terms ....simplify the rest
9 [ ( x - 2)^2 - 84 ] = 0 divide both sides by 9
(x - 2)^2 - 84 = 0
(x - 2)^2 = 84
r = - 2 s = 84
