Exam 14: Quadratic Equations

Solve for all real values of $x: 4=-\frac{x^{-6}+3}{x^{-3}}$

The squares of two consecutive even numbers add to two more than eleven times their sum. What are the numbers?

Solve for $x$ by completing the square: $x^{2}+4 x-5=0$

Solve for all real values of $x$ to three significant digits: $2 x^{4}-4 x^{2}-5=1$

Solve for all real values of $x: x^{\frac{6}{5}}+8=9 \sqrt[5]{x^{3}}$

Solve for all real values of $x: \frac{8-x^{-2}}{x^{-4}}=\frac{x^{-2}-\left(3 x+5 x^{2}\right)}{5}$

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}-4 x+10=0$

A company buys a new pump that can pump $10.0 \mathrm{gal}$ ./min faster than its old one. It can fill the company's 500.0-gallon tank 15.0 minutes faster than the old pump. What was the speed of the old pump?

Determine the area of a right-angle triangle if the difference in the lengths of the shorter sides is $14 \mathrm{~cm}$ and the hypotenuse is $26 \mathrm{~cm}$ .

The difference of two numbers is seven and the product of their cubes is 512 . What are the numbers?

Solve for all real values of $x: x^{6}-28 x^{3}+27=0$