What is the solution to the quadratic equation (x−4)2=16

Question

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Answer 1

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.