Use inspection to solve the equation x2=81

Question

, then select the complete solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)
Responses

{−9}
left brace negative 9 right brace

{−9,9}
left brace negative 9 comma 9 right brace

There are no real solutions.
There are no real solutions.

{9}

Answer 1

To solve the equation $x^2=81$ by inspection, we can determine what value of $x$ makes this equation true.

We know that:

• $9^2=81$
• $(-9{)}^2=81$

Therefore, the solutions to the equation $x^2=81$ are $x=9$ and $x=-9$.

The complete solution set is:

$$-9,9$$

So, the correct response is:

{−9,9}

Answer 2

Use inspection to solve the equation x2=36169
, then select the correct solution set below. If there are no real solutions, select “There are no real solutions.”(1 point)
Responses

{−613,613}
left brace negative Start Fraction 6 over 13 End Fraction comma Start Fraction 6 over 13 End Fraction right brace

There are no real solutions.
There are no real solutions.

{613}
left brace Start Fraction 6 over 13 End Fraction right brace

{−613}

Answer 3

To solve the equation $x^2=36169$ by inspection, we need to find the square root of $36169$.

Calculating the square root:

$$\sqrt{36169}=613$$

Since both $613$ and $-613$ are valid solutions for the equation $x^2=36169$, the complete solution set is:

$$-613,613$$

However, this specific option is not present in your provided responses.

Since there is no correct option listed that matches $-613,613$, if the options provided are the only ones available, and given the absence of the correct set, the only reasonable conclusion is that:

There are no real solutions.

Please verify the options provided. The correct answer should indeed reflect the solutions $-613,613$.

Answer 4

Solve the following quadratic equation using square roots: (x−18)2=196
.(1 point)
Responses

​ {−4,−32}
​ left brace negative 4 comma negative 32 right brace

{21,5}
left brace 21 comma 5 right brace

{32,4}
left brace 32 comma 4 right brace

{214,−178}

Answer 5

To solve the quadratic equation $(x-18{)}^2=196$ using square roots, we can start by taking the square root of both sides of the equation:

1. Take the square root: $$x-18=\pm \sqrt{196}$$

2. Compute the square root: $$\sqrt{196}=14$$ This gives us two equations: $$x-18=14\text{and}x-18=-14$$

3. Solve for $x$ in each case:

   • For $x-18=14$: $$x=14+18=32$$

   • For $x-18=-14$: $$x=-14+18=4$$

Thus, the solutions are $x=32$ and $x=4$.

The complete solution set is: $$32,4$$

The correct response is:

{32,4}

Answer 6

Solve the following quadratic equation using square roots: (x+6)22=8
.(1 point)
Responses

{−1.17,−6.83}
left brace negative 1.17 comma negative 6.83 right brace

{10,−22}
left brace 10 comma negative 22 right brace

​ {−0.34,−11.66}
​ left brace negative 0.34 comma negative 11.66 right brace

{−2,−10}

Answer 7

To solve the quadratic equation $(x+6{)}^2=8$ using square roots, follow these steps:

1. Take the square root of both sides of the equation: $$x+6=\pm \sqrt{8}$$

2. Simplify $\sqrt{8}$: $$\sqrt{8}=\sqrt{4\cdot 2}=2\sqrt{2}$$ So, we have: $$x+6=\pm 2\sqrt{2}$$

3. Solve for $x$:

   • For $x+6=2\sqrt{2}$: $$x=2\sqrt{2}-6$$

   • For $x+6=-2\sqrt{2}$: $$x=-2\sqrt{2}-6$$

Now we can calculate the approximate values:

• Calculate $2\sqrt{2}\approx 2\times 1.414\approx 2.828$: $$x\approx 2.828-6=-3.172$$

• Calculate $-2\sqrt{2}\approx -2.828$: $$x\approx -2.828-6=-8.828$$

Thus, the approximate solutions are:

• $x\approx -3.17$
• $x\approx -8.83$

Now, let us restate them more precisely with first decimal approximations:

• $x\approx -3.17$ and $x\approx -8.83$.

Based on the given options:

• The closest response would be $-0.34,-11.66$, but it doesn't match our calculated values.

There seems to be a mistake in the responses as the closest approximation doesn't match the correct calculations.

After checking the calculations again:

1. We found roots approximately at $-3.17,-8.83$.

None of the provided responses correctly reflect the solved values. Please re-check the options and calculations given.

Answer 8

Solve the following quadratic equation using square roots: (x+36)2−38=251
.(1 point)
Responses

{253,−325}
left brace 253 comma negative 325 right brace

{17.84,−13.84}
left brace 17.84 comma negative 13.84 right brace

{53,19}
left brace 53 comma 19 right brace

{−19,−53}

Answer 9

To solve the quadratic equation $(x+36{)}^2-38=251$ using square roots, follow these steps:

1. Isolate the squared term: $$(x+36{)}^2=251+38$$ $$(x+36{)}^2=289$$

2. Take the square root of both sides: $$x+36=\pm \sqrt{289}$$

3. Calculate the square root: $$\sqrt{289}=17$$ Therefore, we have: $$x+36=17\text{or}x+36=-17$$

4. Solve for $x$:

   • For $x+36=17$: $$x=17-36=-19$$

   • For $x+36=-17$: $$x=-17-36=-53$$

Thus, the solutions are: $$x=-19\text{and}x=-53$$

The complete solution set is: $$-19,-53$$

So, the correct response is:

{−19,−53}