# Chapter 6 Rational Exponents and Radical Functions - Cumulative Review Chapters 1-6 - Page 474: 10

No real solutions

#### Work Step by Step

Using the quadratic equation to solve the equation, we find: $$x_{1,\:2}=\frac{-\left(-6\right)\pm \sqrt{\left(-6\right)^2-4\cdot \:4\cdot \:9}}{2\cdot \:4}$$ The value under the radical is negative, so there are no real solutions. The imaginary solutions are: $$x=\frac{3}{4}+i\frac{3\sqrt{3}}{4},\:x=\frac{3}{4}-i\frac{3\sqrt{3}}{4}$$

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