complete the square...
x^2-16x+4=0
x^2 - 16x + 4 = 0
x^2 - 16x = -4
(-16^2)/4 = 256/4 = 64
x^2 - 16x + 64 = -4 + 64
x^2 - 16x + 64 = 60
(x - 8)^2 = 60
To complete the square for the quadratic equation x^2 - 16x + 4 = 0, follow these steps:
Step 1: Make sure the coefficient of the x^2 term is 1. In this case, it is already 1.
Step 2: Move the constant term to the right side of the equation:
x^2 - 16x = -4
Step 3: Take half of the coefficient of the x term (-16/2 = -8), square it (-8)^2 = 64, and add it to both sides of the equation:
x^2 - 16x + 64 = -4 + 64
Simplifying the right side gives:
x^2 - 16x + 64 = 60
Step 4: Rewriting the left side as a perfect square:
(x - 8)^2 = 60
Step 5: Take the square root of both sides of the equation:
x - 8 = ±√60
Step 6: Solve for x by adding 8 to both sides:
x = 8 ± √60
So the solutions to the quadratic equation x^2 - 16x + 4 = 0 are x = 8 + √60 and x = 8 - √60.