Solve quadratics by inspection, square roots, completing the square, formula, and factoring; express complex solutions.
Solve a quadratic equation using the quadratic formula
Problem
Solve \(x^{2}-5x+6=0\) using the quadratic formula. Identify \(a\), \(b\), and \(c\) with their signs, evaluate the discriminant, and simplify both branches into the complete solution set.
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What this problem is really about
The quadratic formula works from the signed coefficients in standard form, so sign accuracy matters from the start. We’ll identify a, b, and c, substitute them into the full formula, simplify the discriminant first, and then evaluate both the plus and minus branches and check each root.
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