Completing the square rewrites x² + bx as (x + b/2)² minus a constant, so you can read a vertex or a circle center. Factoring is faster when the numbers are clean. This method is for when they are not. Quadratics overall are in quadratic equations.
The move
For x² + 6x, take half of 6, which is 3, and square it, which is 9. Then x² + 6x = (x + 3)² − 9. For x² + bx + c = 0, move c, complete the square, and take square roots. If the leading coefficient is not 1, factor it out first.
The quadratic formula is completing the square done once and frozen. That version is in the quadratic formula. Factoring when it splits nicely is in factoring quadratics.
Circles
Expanded circle equations turn into (x − h)² + (y − k)² = r² by the same step. Circle form is in circle problems.
The bottom line
Half the middle term, square it, add and subtract that square, then write a perfect square.
Start practicing
Start with a free diagnostic, then drill your weak spots with 15-question quizzes and track how you're doing across Reading, English, and Math. Compare plans whenever you're ready to go further.
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