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Completing the square and the quadratic formula
Free examples and worked answers. No account needed.
Practise the method.
Completing the square and the quadratic formula
Optional extension. Solve quadratics with exact surd roots, using completing the square and the quadratic formula.
Example 1
x2−8x+10=0
Show worked answer
Answer: x=4+√6x=4−√6
- Move the constant: x2−8x=−10.
- Add 16 to both sides to complete the square: (x−4)2=6.
- Take both square roots: x−4=±√6.
- Therefore x=4+√6 or x=4−√6.
- Enter both roots, in either order.
Example 2
x2+8x+9=0
Show worked answer
Answer: x=−4+√7x=−4−√7
- Move the constant: x2+8x=−9.
- Add 16 to both sides to complete the square: (x+4)2=7.
- Take both square roots: x+4=±√7.
- Therefore x=−4+√7 or x=−4−√7.
- Enter both roots, in either order.
Example 3
x2−7x+7=0
Show worked answer
Answer: x=27+√21x=27−√21
- Write x2−7x=−7.
- Half the x coefficient is 2−7;
- its square is 449.
- Add 449 to both sides: (x−27)2=421.
- Take both square roots
- subtract 2−7:x=27±√21.
- Therefore x=27+√21 or x=27−√21.
- Enter both roots, in either order.
Put it into practice.
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