Equations
Solving quadratics by completing the square worksheets
Solve ten quadratic equations by completing the square. Choose easy, hard or mixed equations and rational-only answers or exact radical roots.
Preview and downloadEquations practice
Solving quadratics with the quadratic formula worksheets
Solve ten quadratic equations with the quadratic formula. Practice original monic and nonmonic equations with rational and exact radical answers.
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Move the equation to standard form, use the displayed coefficients in the quadratic formula and give every exact real root.
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Customize this worksheetUse an exact quadratic method and keep every real root
Move every term to the left before applying the selected method. Completing the square rewrites the expression as a squared binomial; the quadratic formula substitutes the displayed standard-form coefficients. Both routes preserve exact rational and radical roots.
Each sheet balances five monic and five nonmonic displays and includes one repeated root. Radical practice includes four irrational conjugate pairs. Keys show the reduced root set and one compact cue using the original displayed equation.
Learning objective
What this activity builds
Substitute the standard-form coefficients into the quadratic formula and simplify every exact real root.
Worked example
Solve 2x² + 4x − 1 = 0.
x = −1 ± √6/2.
The discriminant is 24. Substitute a = 2, b = 4 and c = −1, then simplify √24 to 2√6 and reduce the fraction.
Teaching notes
Make the practice count
- Include the sign of b when substituting −b.
- Calculate the discriminant before simplifying the fraction.
- Keep nonsquare roots exact.
- Use the original moved-left coefficients in the substitution.
Make it yours
Customize the practice
Choose your options, update the preview, then download the exact same pages.
Every sheet balances monic and nonmonic equations, includes one repeated root and keeps rational or radical answers exact.
Enlarged pages scroll. PDF size stays the same.
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