Section A.5 – Solving Equations
- 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
Exercises
Directions: You should try to solve each problem first, and then click "Reveal Answer" to check your answer. You can click "Watch Video" if you need help with a problem.
1. Solve the equation by using the quadratic formula. \(4x^2=4x-3\)
\(x=\dfrac{1\pm \sqrt{2} i}{2}\)
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 \(\quad x=-\dfrac{1}{3}\pm\dfrac{\sqrt{10}}{3}\)
4. Solve the equation \(\dfrac{7}{2x+1}-\dfrac{8x}{2x-1}=-4\) and check your solution(s).
\(x=\dfrac{11}{6}\)