What you’ll learn
Solve quadratics using square roots.
Key idea
A positive squared value has two real signed branches; retain both before undoing the shift.
Retain positive and negative square-root branches before undoing the shift; a valid single branch is not the complete solution set.
Worked example
Enter the exact value or ordered values in the format requested below.
Solve (x+4)²=9; enter both numerical roots separated by a comma.
- Both square-root branches are x+4=+3 or x+4=-3.
- Undo the shift in both branches: roots -7, -1; substituting either yields square 9.
Answer: -7, -1
Quick Check
Evaluate a worked attempt at solve quadratics using square roots, identify the first invalid step, and provide the correction.
Solve (x+1)²=49: Step 1 keeps only x+1=+7. Step 2 reports x=6. Locate the first invalid step and correct the full root set.