Solve for y (y+d)^2+(5+d)^2=150^2

${(y + d)}^{2} + {(5 + d)}^{2} = 150^{2}$

Step 1

Subtract ${(5 + d)}^{2}$ from both sides of the equation.

${(y + d)}^{2} = 150^{2} - {(5 + d)}^{2}$

Step 2

Take the specified root of both sides of the equation to eliminate the exponent on the left side.

$y + d = \pm \sqrt{150^{2} - {(5 + d)}^{2}}$

Step 3

Simplify $\pm \sqrt{150^{2} - {(5 + d)}^{2}}$ .

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = 150$ and $b = 5 + d$ .

$y + d = \pm \sqrt{(150 + 5 + d) (150 - (5 + d))}$

Simplify.

Add $150$ and $5$ .

$y + d = \pm \sqrt{(155 + d) (150 - (5 + d))}$

Apply the distributive property.

$y + d = \pm \sqrt{(155 + d) (150 - 1 \cdot 5 - d)}$

Multiply $- 1$ by $5$ .

$y + d = \pm \sqrt{(155 + d) (150 - 5 - d)}$

Subtract $5$ from $150$ .

$y + d = \pm \sqrt{(155 + d) (145 - d)}$

Step 4

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$y + d = \sqrt{(155 + d) (145 - d)}$

Subtract $d$ from both sides of the equation.

$y = \sqrt{(155 + d) (145 - d)} - d$

Next, use the negative value of the $\pm$ to find the second solution.

$y + d = - \sqrt{(155 + d) (145 - d)}$

Subtract $d$ from both sides of the equation.

$y = - \sqrt{(155 + d) (145 - d)} - d$

The complete solution is the result of both the positive and negative portions of the solution.

$y = \sqrt{(155 + d) (145 - d)} - d$

$y = - \sqrt{(155 + d) (145 - d)} - d$

$y = \sqrt{(155 + d) (145 - d)} - d$

$y = - \sqrt{(155 + d) (145 - d)} - d$

Solve for y (y+d)^2+(5+d)^2=150^2

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