Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Solve a quadratic equation by taking square roots
Problem
Solve \(x^{2}=36\) by taking square roots. Include both branches of the square-root operation and state the complete solution set.
Big Picture
What this problem is really about
The squared variable is already isolated, so the square-root property is the most direct method. We’ll take both the positive and negative square-root branches, simplify the root, and verify each value by squaring so the complete solution set is preserved.
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