What you’ll learn
Solve by completing square.
Key idea
Square half the signed linear coefficient and add that same amount to both sides.
Add the squared half-coefficient to both sides, verify completion and then retain both root branches.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve x²-8x+7=0 by completing the square. Enter both roots separated by a comma.
- Move constant: x²-8x=-7; add 16 to both sides, giving (x-4)²=9.
- Both square-root branches x-4=±3 yield complete roots 1, 7.
Answer: 1, 7
Quick Check
Evaluate a worked attempt at solve by completing square, identify the first invalid step, and provide the correction.
Solve x²+4x-45=0: Step 1 gives x²+4x=45. Step 2 adds 2 instead of its square and claims (x+2)²=47. Locate the first invalid step and repair the completed equation and roots.