How do you solve #x^2 - 4x - 7 = 0# by completing the square?

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Answer 1 · 2016-10-05T14:41:42

#(x-2)^2=11#

The process of completing the square converts the quadratic equation into a perfect square trinomial.

First move the constant, #7# to the other side of equation by addition.

#x^2-4x=7#

Next take the coefficient of the #x# term and divide it by 2 and then square it.

#(-4/2)^2=(-2)^2=4#

#4# is amount needed to make the equation into a perfect square trinomial. Add #4# to both sides of the equation to keep it balanced.

#x^2-4x+4=7+4#

Simplify

#x^2-4x+4=11#

Condense the equation

#(x-2)^2=11#

Check out this tutorial on completing the square graphically.

Check out this tutorial on completing the square analytically.