Definition: Complete the Square is a technique used to solve quadratics where the portion of the equation with the independent variable is separated and expressed as the square of a binomial.
Example: Complete the square in x² + 4x + 9.
Step 1: Separate the independent variable.
(x² + 4x) + 9
Step 2: Take half the coefficient of x and square it.
(4/2) = 2, 2² = 4
Step 3: Complete the square by adding 4 as the new constant to the separated x-terms. Be sure to subtract it from the 9 at the end so the value of the expression remains unchanged (since + 4 – 4 = 0).
(x² + 4x + 4) + 9 – 4
(x² + 4x + 4) + 5
Step 4: Express the separated portion in the form (x + a)² where a is half the coefficient of x.
(x + 2)² + 5
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