Question

Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)^2/9=
Answer
WRONG
Answer
STILL WRONG
Answer
Solve the following quadratic equation using square roots. Round to the nearest hundredth if necessary: (x+16)29=7
.(1 point)
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Incorrect

When you have a denominator, make sure to multiply it out before finding the square roots.
Answered by GPT-4o mini
To solve the equation \(\frac{(x + 16)^2}{9} = 0\), we first multiply both sides by 9 to eliminate the fraction:

\[
(x + 16)^2 = 0
\]

Next, we take the square root of both sides:

\[
x + 16 = 0
\]

Now, we solve for \(x\) by subtracting 16 from both sides:

\[
x = -16
\]

Thus, the solution to the equation is

\[
\boxed{-16}
\]

This is an exact answer and does not require rounding.
Answered by GPT-4o mini
I apologize for any confusion. Let's go through the problem step by step to clarify.

The equation given was:

\[
\frac{(x + 16)^2}{9} = 0
\]

Let's solve it again correctly.

1. **Multiply both sides by 9**:

\[
(x + 16)^2 = 0
\]

2. **Take the square root of both sides**:

\[
x + 16 = 0
\]

3. **Solve for \(x\)**:

\[
x = -16
\]

So the solution to the equation \(\frac{(x + 16)^2}{9} = 0\) is indeed:

\[
\boxed{-16}
\]

If this was not the equation you were intending to solve, please clarify the equation, and I'll be happy to assist!
Answered by GPT-4o mini
I apologize for any misunderstanding earlier. It seems there may have been confusion about the original equation you provided. It looks like part of it might have been missing after the equal sign. Let’s clarify and solve the equation correctly.

Please provide the complete equation so I can assist you properly. If I misunderstood the statement and you meant to have something after the equal sign, please include that. Thank you!
Answered by GPT-4o mini
Thank you for your patience. Let's solve the given equation step by step:

The equation provided is:

\[
(x + 16)29 = 7
\]

### Step 1: Divide by 29

First, we want to isolate \(x + 16\). We'll divide both sides by 29:

\[
x + 16 = \frac{7}{29}
\]

### Step 2: Subtract 16 from both sides

Next, we subtract 16 from both sides:

\[
x = \frac{7}{29} - 16
\]

To perform the subtraction, we should convert 16 to a fraction with a common denominator of 29:

\[
16 = \frac{16 \times 29}{29} = \frac{464}{29}
\]

Now we can perform the subtraction:

\[
x = \frac{7}{29} - \frac{464}{29} = \frac{7 - 464}{29} = \frac{-457}{29}
\]

### Step 3: Simplify the result

Dividing \(-457\) by \(29\):

\[
x = -15.79 \quad \text{(rounded to the nearest hundredth)}
\]

### Final Answer

So the solution to the equation is:

\[
\boxed{-15.79}
\]

Let me know if you need further assistance!