A shifted square adds one move to the square root method: after rooting both sides, the shift inside the bracket has to be undone. These free printable worksheets solve (x − h)² = k, and each one still has two answers.
Ready to printSolving (x − h)² = k by square roots
The answer key prints on a separate page.
What's on this sheet
The square is already isolated, so the first move is the same as the bare case — take the root of both sides — but here it leaves x − h = ±√k rather than x by itself. For (x − 2)² = 9 that is x − 2 = ±3, and then the shift is undone by adding 2, giving x = 5 and x = −1. The ± carries through both branches, so the +3 and the −3 each finish as their own answer, and every step-by-step walk here keeps the two apart from the moment the root is taken.
Why this sheet works
This is the reason it is a separate sheet from x² = p: the subtraction inside the bracket means the root does not land on x directly, and a child has to resist reading the answer off before undoing the shift. Meeting it after the bare square is secure keeps the ± habit and the new undo-the-shift step from tangling.
How this one works
One question from this sheet, worked through a step at a time.
Solve (x − 4)² = 81
x − 4 = ±9
x = 4 ± 9
x = 13orx = −5
Take the square root of both sides — both signs: x − 4 = ±√81 = ±9.
1. (x − 4)² = 81 → x = −5 or x = 132. (x + 3)² = 4 → x = −5 or x = −13. (x − 8)² = 100 → x = −2 or x = 184. (x − 8)² = 16 → x = 4 or x = 125. (x − 5)² = 36 → x = −1 or x = 116. (x − 3)² = 49 → x = −4 or x = 107. (x − 5)² = 49 → x = −2 or x = 128. (x − 7)² = 1 → x = 6 or x = 89. (x + 8)² = 36 → x = −14 or x = −210. (x − 8)² = 25 → x = 3 or x = 13
