Solving Quadratic Equations Using Square Roots
Solve quadratic equations using square roots in Grade 9 algebra: isolate the squared term, then take the square root of both sides, remembering to include both positive and negative solutions (±).
Key Concepts
New Concept Quadratic equations in the form $x^2 = a$ can be solved by taking the square root of both sides. What’s next Next, you’ll isolate the squared variable and use this principle to solve equations, finding both exact and approximate answers for various problems.
Common Questions
How do you solve a quadratic equation using the square root method?
Isolate the squared variable on one side of the equation. Then take the square root of both sides. Always include ± to capture both solutions. For x² = 49, taking square roots gives x = ±7.
What types of quadratic equations are best solved with square roots?
Equations of the form ax² = c or (x + k)² = c, where no linear term (bx) is present, are ideal for the square root method. If there is a linear term, factoring or the quadratic formula is more appropriate.
Why must you write ± when solving quadratic equations with square roots?
Both positive and negative values square to the same positive result. So x² = 25 has two solutions: x = 5 AND x = -5. Omitting the negative answer means missing half the solution set.