What is the solution to the quadratic equation (x−4)2=16
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To find the solution to the quadratic equation (x-4)² = 16, we need to first expand the left side of the equation.
(x-4)² = (x-4)(x-4)
= x² - 4x - 4x + 16
= x² - 8x + 16
Now, we can set this expanded expression equal to 16:
x² - 8x + 16 = 16
Subtracting 16 from both sides gives:
x² - 8x = 0
Factor out an x from the equation:
x(x - 8) = 0
Now, we set each factor equal to zero and solve for x:
x = 0 or x - 8 = 0
x = 0 or x = 8
Therefore, the solutions to the quadratic equation are x = 0 and x = 8.