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.
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Solving quadratics by taking square roots worksheets
Solve ten quadratic equations by isolating a squared variable and taking both square roots. Choose direct, offset, scaled, multi-step or mixed equations with rounded real, exact real, no-real or imaginary results.
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Isolate the squared variable, then take both square roots. Follow the selected real or imaginary domain and rounding instruction.
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Customize this worksheetIsolate the square, then take both roots
Direct questions begin with the square isolated. Offset, scaled and multi-step questions require one or two inverse operations first. The problem selector controls equation structure independently from the real or imaginary solution domain.
The key shows the exact isolation value before the complete solution. Nonzero roots include both signs, zero appears once, rounded noninteger real roots use an approximation sign, and negative squared values become either No real solution or exact imaginary roots according to the selected domain.
Learning objective
What this activity builds
Isolate the squared variable and use both square roots to give the complete real or imaginary solution set.
Worked example
Solve 3x² + 2 = 20.
x = ±√6.
Subtract 2 and divide by 3 to obtain x² = 6. Taking both square roots gives x = ±√6.
Teaching notes
Make the practice count
- Isolate the squared expression before taking a root.
- Write both signs for every nonzero squared value.
- Write zero once rather than ±0.
- Keep exact radicals simplified and denominators rationalized.
- Use No real solution only when the selected domain is real.
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Customize the practice
Choose your options, update the preview, then download the exact same pages.
Every ten-question sheet isolates the squared variable first. Choose the equation structure independently from the real, no-real or imaginary answer domain.
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