Completing The Square
Key points
- Completing the square is another method to solve for the solutions of a quadratic function.
- When the quadratic is in standard form and set equal to 0:
- Take the b coefficient.
- Divide it by 2
- Square it
- Add it after terms a and b, and subtract it from c.
- Solve for x
Completing the square is an alternative algebraic method to the quadratic formula and to factorizing.
- It is best to use when the leading coefficient is 1, and the coefficient of the middle term is an even number.
- In general, follow the structure seen to the right.
An algebraic series of steps to replicate the structure seen above:
- Take the b coefficient.
- Divide it by 2
- Square it
- Add it after terms a and b, and subtract it from c.
- Once you have simplified, you have completed the square.
- Solve for x by setting the factor expression and the independent value equal to each other, then finding the square root of each side to solve.
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