Quiz about Solve Quadratic by Completing the Square

Question 1

John is planning to build a rectangular garden and he wants the area of the garden to be represented by the quadratic equation $$x^2 + 10x + 16 = 0$$ . To determine the possible dimensions (x) of the garden, he needs to solve this equation. Complete the square to find the value of x.

Accepted Answer

$$x = -5 \pm \sqrt{9}$$

Answer

$$x = -5 \pm \sqrt{1}$$

Answer

$$x = 5 \pm \sqrt{9}$$

Answer

$$x = 5 \pm \sqrt{1}$$

Question 2

A farmer is planning to create a rectangular enclosure for her sheep. She wants the area of the enclosure to be represented by the quadratic equation $$2x^2 - 8x - 10 = 0$$ , where $$x$$ is the length of the enclosure in meters. Help her determine the possible lengths of the enclosure by completing the square.

Accepted Answer

$$x = 2 \pm \sqrt{12}$$

Answer

$$x = 2 \pm \sqrt{5}$$

Answer

$$x = 4 \pm \sqrt{12}$$

Answer

$$x = 4 \pm \sqrt{5}$$

Question 3

John is trying to calculate the dimensions of a garden that is shaped like a quadratic equation $$x^2 + 6x + 8 = 0$$ . Help him by completing the square.

Accepted Answer

$$x = -3 \pm \sqrt{1}$$

Answer

$$x = -3 \pm \sqrt{7}$$

Answer

$$x = 3 \pm \sqrt{1}$$

Answer

$$x = 3 \pm \sqrt{7}$$

Question 4

A rocket's trajectory is modeled by the equation $$x^2 - 12x + 27 = 0$$ , where $$x$$ represents the time in seconds after launch, and the equation gives its altitude. To predict the time when the rocket will reach its peak altitude, complete the square.

Accepted Answer

$$x = 6 \pm \sqrt{9}$$

Answer

$$x = 6 \pm \sqrt{12}$$

Answer

$$x = 6 \pm \sqrt{15}$$

Answer

$$x = 6 \pm \sqrt{18}$$

Solve Quadratic by Completing the Square

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