How do you solve using the completing the square method #x^2 - 4x =12 #?

Question

Abigail Allen · Accepted Answer

#y=(x-2)^2-16# Set the equation's initial value to 0. #x^2-4x-12=0# Now finish the square. #[x^2-4x]-12# #[(x-2)^2-4]-12# #(x-2)^2-4-12# #(x-2)^2-16#

Ethan Adkins · Answer

undefined To solve the quadratic equation $x^2 - 4x = 12$ using the completing the square method, first, move the constant term to the other side of the equation to set it equal to zero: $x^2 - 4x - 12 = 0$. Then, add the square of half the coefficient of x (which is $(-4/2)^2 = 4$) to both sides of the equation to complete the square: $x^2 - 4x + 4 = 12 + 4$. Simplify both sides: $x^2 - 4x + 4 = 16$. Rewrite the left side as a squared binomial: $(x - 2)^2 = 16$. Take the square root of both sides: $x - 2 = \pm \sqrt{16}$. Solve for x: $x - 2 = \pm 4$. Add 2 to both sides: $x = 2 \pm 4$. So, the solutions are $x = 2 + 4$ and $x = 2 - 4$, which simplify to $x = 6$ and $x = -2$.