complete the square identity the two values that solve the following quadratic equation: x^2 + 8x = 9
To complete the square for the quadratic equation x^2 + 8x = 9, we need to add and subtract the square of half the coefficient of the x term.
The coefficient of x in this equation is 8, so half of 8 is 4, and the square of 4 is 16.
By adding and subtracting 16, the equation becomes:
x^2 + 8x + 16 - 16 = 9
(x^2 + 8x + 16) - 16 = 9
(x + 4)^2 - 16 = 9
Now, rearranging the equation to isolate the perfect square:
(x + 4)^2 = 9 + 16
(x + 4)^2 = 25
Taking the square root of both sides of the equation:
x + 4 = ±√25
x + 4 = ±5
Solving for x:
1. x = -4 + 5 = 1
2. x = -4 - 5 = -9
Therefore, the two values that solve the quadratic equation x^2 + 8x = 9 are x = 1 and x = -9.