Completing the Square Calculator
Rewrite ax² + bx + c as a(x − h)² + k. Enter numerical coefficients with a nonzero leading coefficient.
Formula
h = −b/(2a); k = c − b²/(4a); ax² + bx + c = a(x − h)² + k.
Multiplier a ≈ (1) · Shift h ≈ -(6)÷(2×(1)) · Constant k ≈ (5)-(6)^2÷(4×(1))
How to use
- Enter a, b and c.
- Use a ≠ 0; negative coefficients are allowed.
- Insert the displayed a, h and k into a(x − h)² + k.
Examples
- x² + 6x + 5 = (x + 3)² − 4.
Frequently asked questions
What if h is negative?
Subtracting a negative means adding: h = −3 gives (x + 3)².
Does this solve an equation?
It rewrites the polynomial. Use the quadratic equation tool for roots.
Why is a = 0 rejected?
The expression would be linear, so the quadratic completing-square formula does not apply.
Sources
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