Quadratic Equations • Topic 3 of 5

Square Root Method

When a quadratic has no linear (x) term, or can be written as a square equal to a number, take square roots directly — remembering both signs. From x² = 25 you get x = ±5; from (x − 2)² = 9 you get x − 2 = ±3, so x = 5 or x = −1. Isolate the squared quantity first, then apply ±√ to both sides. If the number is negative, there are no real solutions. The square-root method is the quickest route for "pure" quadratics and for equations already in vertex-like form, both common on the SAT.

✅ Solved examples

1. Solve x² = 49.
Take square roots: x = ±7.
2. Solve x² − 20 = 5.
x² = 25, so x = ±5.
3. Solve (x − 1)² = 16.
x − 1 = ±4, so x = 5 or x = −3.
4. Solve 2x² = 50.
x² = 25, so x = ±5.

✏️ Practice — try these, take hints as needed

1. Solve x² = 81.
Take square roots of both sides.
Include ±.
—
x = ±9.
2. Solve x² + 4 = 29.
Subtract 4: x² = 25.
Square root.
—
x = ±5.
3. Solve (x + 2)² = 9.
x + 2 = ±3.
Solve each case.
—
x = 1 or x = −5.
4. Solve 3x² = 27.
Divide by 3: x² = 9.
Square root.
—
x = ±3.
5. Solve (x − 5)² = 4.
x − 5 = ±2.
Solve each case.
—
x = 7 or x = 3.

📝 Topic test — 8 questions

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