Exam 14: Quadratic Equations

Solve for $x$ and $y: x^{2}-2 x y+2 y^{2}=20$ $x-y=2$

Solve for $x$ and $y: x^{2}-y^{2}=21$ $x-y=3$

Solve for $x$ by factoring: $8 x^{2}=3 x$

Solve for $x$ in terms of $y: 2 x^{2}+x y-y^{2}=0$

Solve for $x$ by factoring: $x^{2}+14 x+45=0$

Solve for $x$ and $y: \frac{1}{x}-\frac{1}{y}=\frac{2}{3}$ $x+y=4$

A woman starts out with $\$ 10,000$ . One year, the government takes a certain percentage $t$ of this money. The next year, the government takes the same percentage out of the remainder of the woman's money. She is left with $\$ 8,100$ . What is the percentage $t$ ?

Use the quadratic formula to solve for $x$ to three significant digits: $x^{2}+6 x-9=0$

Use the quadratic formula to solve for $x$ to three significant digits: $3(x+1)+(x-1)^{3}=(x+1)^{3}$

Solve for $x$ by factoring: $7 x=\frac{28}{x+3}$

Solve for all real values of $x: x^{4}-29 x^{2}+100=0$

Solve for all real values of $x: x^{\frac{6}{5}}-7=6 \sqrt[5]{x^{3}}$

Double a certain whole number divided by the next biggest whole number is two less than triple the number. What is the number?

Solve for $x$ by completing the square: $6 x^{2}-5 x-6=0$

For a chemical reaction $\mathrm{C}_{2} \mathrm{H}_{4}+\mathrm{H}_{2} \rightleftharpoons \mathrm{C}_{2} \mathrm{H}_{6}$ , the equilibrium concentration of the reactant $\mathrm{C}_{2} \mathrm{H}_{4}$ is given by $0.335-x$ and the equilibrium concentration of the reactant $\mathrm{H}_{2}$ is given by $0.526-x$ , where $\frac{x}{(0.335-x)(0.526-x)}=0.990$ . Determine the equilibrium concentrations of each reactant.

In a certain number of hours, a man travelled $48.0 \mathrm{~km}$ . If his speed had been $2.00 \mathrm{~km} / \mathrm{h}$ faster, it would have saved him $3.00 \mathrm{~h}$ . What was his speed?

Solve for $x$ and $y: \frac{x^{2}+y^{2}}{x y}=\frac{5}{2}$ $x^{2}-y^{2}=3$

Use the quadratic formula to solve for $x$ to three significant digits: $9 x^{2}+3 x+1=0$

Solve for $x$ and $y: \frac{x+y}{x-y}=\frac{3}{2}$ $x y=80$

Plot $y = 4x^2 ? 4x ? 3$ and label the vertex.