Solve Quadratic and rational Equations

Solve a set of problems, with detailed solutions, related to quadratic and some of the questions have rational equations. A set of 10 problems in this page have detailed solutions.

You may prefer to go through a tutorial on Equations with Rational Expressions before you start solving the following equations.

Problem 1: Find all real solution to the quadratic equation

x2 + 2x = -1

Detailed Solution.

Problem 2: Find all real solution to the quadratic equation

x2 + 2 = x + 5

Detailed Solution.

Problem 3: Find all real solution to the equation

- ( x + 2)(x - 1) = 3

Detailed Solution.

Problem 4: Find all real solution to the rational equation.

(2x + 1) / (x + 2) = x - 1


a:   (1 + sqrt(13) / 2 and (1 - sqrt(13) / 2

Detailed Solution.

Problem 5: Find all real solution to the rational equation.

2 / (x + 1) - 1 / (x - 2) = -1

Detailed Solution.

Problem 6: Find all real solution to the equation.

2(x - 2)2 - 6 = -2

Detailed Solution.

Problem 7: Find all real solution to the rational equation.

x / (x + 4) = -3 / (x - 2) + 18 / (x - 2) (x + 4)

Detailed Solution.

Problem 8: Find all real solution to the quadratic equation.

x2 - 3(x - 3)2 = 2

Detailed Solution.

Problem 9: Find all real solution to the rational equation.

1 / (x - 4) + 1 / (x + 4)= x2 / (x2 - 16)

Detailed Solution.

Problem 10: Find all real solution to the rational equation.

-x / (x + 3) - x / (x - 3) = - 4 / (x2 - 9) - 1 / (x + 3)

Detailed Solution.



More references and links to tutorials and problems on equations.

Solve Quadratic Equations Using Discriminants.
Tutorial on Equations of the Quadratic Form.
Math Problems, Questions and Online Self Tests.
More Intermediate and College Algebra Questions and Problems with Answers.