8.

Question

Solve x2= 25/64
by inspection. There are 2 real solutions. Enter the lesser number first. Leave the answers in simplest fraction form.

(1 point)
The first solution is x=

The second solution is x =

Question 2
9.

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary. List the answer from smallest to largest number.

(x + 27)2/−6 = −3

Here is a number line to help you remember the order of numbers.

(1 point)
The first solution is x=

The second solution is x=

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Answer 1

Question 1: Solve $x^2=\frac{25}{64}$

To find $x$, we take the square root of both sides:

$$x=\pm \sqrt{\frac{25}{64}}$$

Calculating the square root:

$$\sqrt{\frac{25}{64}}=\frac{\sqrt{25}}{\sqrt{64}}=\frac{5}{8}$$

Thus, the two solutions are:

$$x=\frac{5}{8}\text{and}x=-\frac{5}{8}$$

Listing the answers from smallest to largest:

• The first solution is $x=-\frac{5}{8}$
• The second solution is $x=\frac{5}{8}$

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Question 2: Solve the equation $\frac{(x+27{)}^2}{-6}=-3$

First, we clear the fraction by multiplying both sides by -6:

$$(x+27{)}^2=-3\times -6$$ $$(x+27{)}^2=18$$

Now, we take the square root of both sides:

$$x+27=\pm \sqrt{18}$$

Calculating $\sqrt{18}$:

$$\sqrt{18}=\sqrt{9\times 2}=3\sqrt{2}$$

Therefore, we have:

$$x+27=3\sqrt{2}\text{or}x+27=-3\sqrt{2}$$

Now, we solve for $x$:

1. From $x+27=3\sqrt{2}$:

$$x=3\sqrt{2}-27$$

2. From $x+27=-3\sqrt{2}$:

$$x=-3\sqrt{2}-27$$

Next, we approximate $\sqrt{2}$, which is approximately 1.414. Thus:

1. $3\sqrt{2}\approx 3\times 1.414\approx 4.242$ So, $$x\approx 4.242-27\approx -22.758$$

2. $-3\sqrt{2}\approx -4.242$ So, $$x\approx -4.242-27\approx -31.242$$

Rounding to the nearest hundredth:

1. $x\approx -22.76$
2. $x\approx -31.24$

Listing the answers from smallest to largest:

• The first solution is $x\approx -31.24$
• The second solution is $x\approx -22.76$

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Final Answers:

1. Question 1:

   • First solution: $x=-\frac{5}{8}$
   • Second solution: $x=\frac{5}{8}$

2. Question 2:

   • First solution: $x\approx -31.24$
   • Second solution: $x\approx -22.76$