This page contains 10 exercises on quadratic and rational equations with detailed solutions. You can practice solving these equations and refer to the explanations for guidance.
You may want to review our tutorial on Equations with Rational Expressions before attempting the questions.
Find all real solutions to the quadratic equation:
\[x^2 + 2x = -1\]Find all real solutions to the quadratic equation:
\[x^2 + 2 = x + 5\]Find all real solutions to the equation:
\[-(x + 2)(x - 1) = 3\]Find all real solutions to the rational equation:
\[\frac{2x + 1}{x + 2} = x - 1\]Find all real solutions to the rational equation:
\[\frac{2}{x + 1} - \frac{1}{x - 2} = -1\]Find all real solutions to the quadratic equation:
\[2(x - 2)^2 - 6 = -2\]Find all real solutions to the rational equation:
\[\frac{x}{x + 4} = -\frac{3}{x - 2} + \frac{18}{(x - 2)(x + 4)}\]Find all real solutions to the quadratic equation:
\[x^2 - 3(x - 3)^2 = 2\]Find all real solutions to the rational equation:
\[\frac{1}{x - 4} + \frac{1}{x + 4} = \frac{x^2}{x^2 - 16}\]Find all real solutions to the rational equation:
\[-\frac{x}{x + 3} - \frac{x}{x - 3} = -\frac{4}{x^2 - 9} - \frac{1}{x + 3}\]