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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. \(4x^2=4x-3\)

    \(x=\dfrac{1\pm \sqrt{2} i}{2}\)


    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V4

  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 \(\quad x=-\dfrac{1}{3}\pm\dfrac{\sqrt{10}}{3}\)


    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V5

  3. Solve the polynomial equation. \(x^3-3x^2-x=-3\)

    \(x=-1, 1, 3\)


    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V6

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

    \(x=\dfrac{11}{6}\)


    To see the full video page and find related videos, click the following link.
    WIR2 20B M150 V7

  5. Solve the following equation \(x^2+8x+10=0\)

    \(x=-4\pm\sqrt{6}\)


    To see the full video page and find related videos, click the following link.
    WIR8 20B M150 V05