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Question 1

Solve and simplify completely. Exact answers only.

\[2x(x+2)=3\]

Answer: \(\frac{-2\pm \sqrt{10}}{2}\)

Question 2

Solve and simplify completely. Exact answers only.

\[ 4-\frac{1}{x}-\frac{2}{x^2}=0 \]

Answer: \(\frac{1 \pm \sqrt{33}}{8}\)

Question 3

Solve. Your answer must be rounded to 2 decimal places.

\[ \pi x^2-x-\pi=0 \]

Answer: \(-0.85, 1.17\)

Question 4

Solve. Your answer must be rounded to 2 decimal places.

\[ \sqrt{3}x+x^2=3 \]

Answer: \(-2.08, 1.07\)

Question 5

An extra-large chocolate bar with a rectangular shape measures 12 centimeters in length, 7 centimeters in width, and 3 centimeters in thickness. Due to escalating costs of cocoa, management decides to reduce the volume of the bar by 10%. To accomplish this reduction, management decides that the new bar should have the same 3-centimeter thickness, but the length and width of each should be reduced an equal number of centimeters. What are the dimensions of the new candy bar?

Answer: \(11.55\text{ cm long by } 6.55\text{ cm wide by } 3\text{ cm thick}\)