Non-linear equations (one variable)

• x = {-1, 3}

• x = {-3, 1}

• No solution

• x = 1

• 27 or 30

• 9

• No Real Solution

  Imaginary Solutions

Solve by using the quadratic formula.

 $2x^2-3x=-4$  

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Solve. Round to the nearest hundredth.

 $x^2+10x+35=0$  

•  $x=-5\pm6.32i$  

•  $x=-5\pm5i$  

•  $x=-5\pm10i$  

•  $x=-5\pm3.16i$  

 $x^2+5x\ +8\ =0$  

Solve the given equation using the Quadratic Formula. Make sure you fully simplify your answer.

•  $\frac{-5\pm\sqrt{57}}{2}$  

•  $\frac{5\pm\sqrt{57}}{2}$  

•  $\frac{-5\pm i\sqrt{7}}{2}$  

•  $\frac{5\pm i\sqrt{7}}{2}$  

Solve the following quadratic equation by using the quadratic formula:
 $5x^2-7x+11=0$  

•  $x=\frac{-1+i\sqrt{7}}{2}\ \&\ x=\frac{-1-i\sqrt{7}}{2}$  

•  $x=\frac{1+i\sqrt{23}}{2}\ \&\ x=\frac{1-i\sqrt{23}}{2}$  

•  $x=2\ \&\ x=-3$  

•  $x=\frac{7+3i\sqrt{19}}{10}\ \&\ x=\frac{7-3i\sqrt{19}}{10}$  

What are the zeros of the function f(x) = x² + 64?

(In other words, what are the solutions to x² + 64 = 0?)

• -8 and 8
• -8i and 8i
• (-√8) i and (√8) i
• -√8  and √8

Describe the number and type solutions for the following:

 $y=x^2+7x+13$  

• 2 real solutions

• 2 non-real solutions

• 1 real solution

• 1 non-real solution

Solve the equation $3x^2+96=0$  

•  $\pm4\sqrt{2}$  

•  $\pm4i\sqrt{2}$  

•  $2i\sqrt{4}$  

•  $\pm2\sqrt{4}$