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(x+16)^2/9 = 7

solve for x

5 answers

To solve the equation \(\frac{(x + 16)^2}{9} = 7\), follow these steps:

  1. Multiply both sides by 9 to eliminate the fraction: \[ (x + 16)^2 = 7 \cdot 9 \] \[ (x + 16)^2 = 63 \]

  2. Take the square root of both sides: \[ x + 16 = \pm \sqrt{63} \]

    Since \(\sqrt{63} = \sqrt{9 \times 7} = 3\sqrt{7}\), we can rewrite this as: \[ x + 16 = \pm 3\sqrt{7} \]

  3. Solve for \(x\) by subtracting 16 from both sides: \[ x = -16 \pm 3\sqrt{7} \]

Thus, the solutions for \(x\) are: \[ x = -16 + 3\sqrt{7} \quad \text{and} \quad x = -16 - 3\sqrt{7} \]

what is x just tell me

The two solutions for \(x\) are:

  1. \(x \approx -16 + 7.937 = -8.063\)
  2. \(x \approx -16 - 7.937 = -23.937\)

So, approximately,

  • \(x \approx -8.063\)
  • \(x \approx -23.937\)

In exact terms, \(x = -16 + 3\sqrt{7}\) or \(x = -16 - 3\sqrt{7}\).

use inspection to solve the equation x^2 = 36/169, then select the correct solution set below. if there are no solution, elect No solution
A. no solution
B. { - 6/13, 6/13}
C. { 6/13 }
D. {- 6/13 }

To solve the equation \(x^2 = \frac{36}{169}\) using inspection, we can note that we want to find values of \(x\) such that their squares equal \(\frac{36}{169}\).

Taking the square root of both sides, we have: \[ x = \pm \sqrt{\frac{36}{169}}. \]

Simplifying this: \[ x = \pm \frac{\sqrt{36}}{\sqrt{169}} = \pm \frac{6}{13}. \]

So, the solutions are: \[ x = \frac{6}{13} \quad \text{and} \quad x = -\frac{6}{13}. \]

This gives us the solution set: \[ { -\frac{6}{13}, \frac{6}{13} }. \]

Thus, the correct answer is: B. { -6/13, 6/13 }.