What you’ll learn
Solve x² = p.
Key idea
A positive square value has two opposite real solutions, both of which must satisfy the original equation.
A principal radical is not a squared equation's full real solution set; both signs require verification.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve x²=256 over the reals. Enter both solutions as comma-separated numbers, negative first.
- Both (-16)² and (16)² equal 256, so both signed candidates solve x²=256.
- These exhaust the real solutions: the squared equation requires magnitude 16; the inverse right side is p=16²=256.
Answer: -16,16
Quick Check
Evaluate a worked attempt at solve x² = p, identify the first invalid step, and provide the correction.
Solve x²=1681: Step 1 finds principal square-root magnitude 41. Step 2 reports x=41 as the only real solution. Identify the first invalid step and repair the solution set.