# Section A.5 – Solving Equations

Section Details.
• Solving quadratic equations using factoring, completing the square, and the quadratic formula
• Solving polynomial equations by factoring
• Solving rational equations and checking for extraneous solutions
• Solving radical equations and checking for extraneous solutions
• Solving absolute value equations and checking for extraneous solutions

### Practice Problems

Directions. The following are review problems for the section. We recommend you work the problems yourself, and then click "Answer" to check your answer. If you do not understand a problem, you can click "Video" to learn how to solve it.

1. ​Solve the equation by using the quadratic formula. $$4x^2=4x-3$$

$$x=\dfrac{1\pm \sqrt{2} i}{2}$$

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2. Solve the equation $$3x^2+2x-3=0$$ by completing the square.

$$3\left(x+\dfrac{1}{3}\right)^2=\dfrac{10}{3}\quad$$ so $$\quad x=-\dfrac{1}{3}\pm\dfrac{\sqrt{10}}{3}$$

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3. Solve the polynomial equation. $$x^3-3x^2-x=-3$$

$$x=-1, 1, 3$$

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4. Solve the equation $$\dfrac{7}{2x+1}-\dfrac{8x}{2x-1}=-4$$ and check your solution(s).

$$x=\dfrac{11}{6}$$

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5. Solve the following equation $$x^2+8x+10=0$$

$$x=-4\pm\sqrt{6}$$

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