A step by step interactive worksheet to help you develop the skill of completing the square of quadratic expressions. As many examples as needed may be generated interactively and the solutions with explanations are also included.
We use the identity $$(x+b/2)^2 = x^2+bx+(b/2)^2 \, \, \, \, (1)$$ which is equivalent to $$x^2+bx = (x+b/2)^2 - (b/2)^2\, \, \, \, (2) $$ to complete the square. Solve each step below then click on "Show me" to check your answer.
Step by step solution
STEP 1: Rewrite the given equation such that only the terms in $x$ and $x^2$ are on the right.
STEP 2: Divide both sides of the equation obtained in step (1) by the coefficient of $x^2$ and simplify the right side only.
STEP 3: We now use the identity $x^2+bx = (x+b/2)^2 - (b/2)^2$ (see top of page) to rewrite the right side of the above equation as the difference of a square and a constant.
STEP 4: We now rewrite second equation obtained in step (2) using the expression containing the square obtained in step(3).
STEP 5: Multiply and simply the above to rewrite it as $y=a(x-h)^2+k$.
Completeing the square can also be used to solve quadratic equations and
Evaluate Integrals Involving Quadratics Using Completing Square.
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