Algebra 1 / Unit 9: Quadratic Functions and Equations
9.4 Solving with Square Roots
Notes
When a quadratic has no $x$ term, isolate the square and take the square root of both sides. Remember both the positive and negative roots.
- $x^2 = 49 \Rightarrow x = \pm 7$.
- $3x^2 - 12 = 0 \Rightarrow x^2 = 4 \Rightarrow x = \pm 2$.
- $(x - 1)^2 = 25 \Rightarrow x - 1 = \pm 5 \Rightarrow x = 6$ or $x = -4$.
- $x^2 = -9$ has no real solution.
Practice
Solve $x^2 - 81 = 0$.
$x^2 = 81$.
Solve $(x + 2)^2 = 16$.
$x + 2 = \pm 4$.
Solve $2x^2 + 18 = 0$.
$x^2 = -9$, and no real number squared is negative.
Ready for more? Take the Unit 9 test.