Completing the Square Practice worksheet with problems on simplifying radicals, solving equations, and completing the square.

A worksheet titled "Completing the Square Practice" with three sections: simplifying radicals, solving equations for x, and completing the square to solve equations. Includes mathematical expressions and instructions.

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1.
a. √72 = 6√2
b. √80 = 4√5
c. √96 = 4√6
d. √(4/25) = 2/5
e. √(1/4) = 1/2
f. √(11/100) = √11 / 10

2.
a. (x − 3)² = 4 → x − 3 = ±2 → x = 5 or x = 1
b. 2(x + 3)² = 12 → (x + 3)² = 6 → x + 3 = ±√6 → x = −3 ± √6
c. (x − 7)² + 3 = 9 → (x − 7)² = 6 → x − 7 = ±√6 → x = 7 ± √6
d. 2(x + 1)² − 2 = 16 → 2(x + 1)² = 18 → (x + 1)² = 9 → x + 1 = ±3 → x = 2 or x = −4

3.
a. x² + 6x − 12 = 0 → x² + 6x = 12 → x² + 6x + 9 = 21 → (x + 3)² = 21 → x = −3 ± √21
b. x² + 2x − 6 = 0 → x² + 2x = 6 → x² + 2x + 1 = 7 → (x + 1)² = 7 → x = −1 ± √7
c. x² + 2x − 12 = 0 → x² + 2x = 12 → x² + 2x + 1 = 13 → (x + 1)² = 13 → x = −1 ± √13
d. x² + 8x + 5 = 7 → x² + 8x = 2 → x² + 8x + 16 = 18 → (x + 4)² = 18 → x = −4 ± 3√2

Parent Tip: Review the logic above to help your child master the concept of solving quadratic equations by completing the square worksheets.

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