Solving x² + 6x + 2 = 0 by Completing the Square

Algebra 1 · Axiom Academy

EXAMPLE Solving by Completing the Square Solve the quadratic x^2 + 6x + 2 = 0 by completing the square, one step at a time. Solve the equation x^2 + 6x + 2 = 0 for x by completing the square. This quadratic does not factor over the integers, so we will reshape the left side into a perfect square and take a square root. Nice work — you completed the square on x^2 + 6x + 2 = 0 and found both roots. The moves that got you there: Move the constant: get the x -terms alone on one side. Find (b/2)^2 : take half the coefficient of x , then square it — here (6/2)^2 = 9 . Add to both sides: keep the equation balanced. Factor as a perfect square: x^2 + 6x + 9 = (x+3)^2 . Take the square root: don't forget the sign. Solve for x : isolate x to get both solutions, . This method works for any quadratic and is exactly where the quadratic formula comes from. The same steps also rewrite a quadratic into vertex form.

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