Concept

Solving Quadratic Equations with Rational Coefficients Using the Square Root Property

When solving a quadratic equation that contains fractions, the standard procedure using the Square Root Property still applies. First, isolate the quadratic term on one side of the equation. If the squared variable has a rational coefficient, multiply both sides of the equation by the reciprocal of that fraction to make the leading coefficient 1. Once the equation is in the standard form x2=kx^2 = k, apply the Square Root Property to find the potential solutions. Finally, simplify any resulting radicals. For example, to solve 23u2+5=17\frac{2}{3}u^2 + 5 = 17, first isolate the quadratic term to get 23u2=12\frac{2}{3}u^2 = 12. Then, multiply both sides by the reciprocal 32\frac{3}{2} to obtain u2=18u^2 = 18. Applying the Square Root Property gives u=±18u = \pm\sqrt{18}, which simplifies to u=±32u = \pm3\sqrt{2}.

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Updated 2026-05-26

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Ch.9 Quadratic Equations and Functions - Intermediate Algebra @ OpenStax

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