Solve the following quadratic equation using square roots round to the nearest hundredth pig necessary (x+16)2/9=7

Answer 1

To solve the equation \((x + 16)^2/9 = 7\), we will first isolate the term on the left side.

1. Multiply both sides by 9 to eliminate the fraction:

\[ (x + 16)^2 = 7 \times 9 \]

\[ (x + 16)^2 = 63 \]

2. Now, take the square root of both sides:

\[ x + 16 = \pm \sqrt{63} \]

3. Calculate \(\sqrt{63}\). Since \(\sqrt{63} \approx 7.937\), we have:

\[ x + 16 = \pm 7.937 \]

4. Now, isolate \(x\) by subtracting 16 from both sides. This gives us two cases to solve:

Case 1:

\[ x + 16 = 7.937 \]

\[ x = 7.937 - 16 \]

\[ x \approx -8.063 \]

Case 2:

\[ x + 16 = -7.937 \]

\[ x = -7.937 - 16 \]

\[ x \approx -23.937 \]

Thus, the solutions to the equation \((x + 16)^2/9 = 7\) are:

\[ x \approx -8.06 \quad \text{and} \quad x \approx -23.94 \]

Rounded to the nearest hundredth, the final answers are:

\[ x \approx -8.06 \quad \text{and} \quad x \approx -23.94 \]

Answer 2

(X-6)2=51

Answer 3

To solve the equation \((x - 6)^2 = 51\), we can follow these steps:

1. Take the square root of both sides:

\[ x - 6 = \pm \sqrt{51} \]

2. Calculate \(\sqrt{51}\). The approximate value is:

\[ \sqrt{51} \approx 7.14 \]

3. Now, we have two cases to solve:

Case 1:

\[ x - 6 = \sqrt{51} \]

\[ x = 6 + \sqrt{51} \approx 6 + 7.14 \approx 13.14 \]

Case 2:

\[ x - 6 = -\sqrt{51} \]

\[ x = 6 - \sqrt{51} \approx 6 - 7.14 \approx -1.14 \]

Thus, the solutions to the equation \((x - 6)^2 = 51\) are:

\[ x \approx 13.14 \quad \text{and} \quad x \approx -1.14 \]

Rounded to the nearest hundredth, the final answers are:

\[ x \approx 13.14 \quad \text{and} \quad x \approx -1.14 \]