Algebra Examples

$x = {(y - 3)}^{2} + 41$

Step 1

Solve for $y$ .

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Step 1.1

Rewrite the equation as ${(y - 3)}^{2} + 41 = x$ .

${(y - 3)}^{2} + 41 = x$

Step 1.2

Subtract $41$ from both sides of the equation.

${(y - 3)}^{2} = x - 41$

Step 1.3

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

$y - 3 = \pm \sqrt{x - 41}$

Step 1.4

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

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Step 1.4.1

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

$y - 3 = \sqrt{x - 41}$

Step 1.4.2

Add $3$ to both sides of the equation.

$y = \sqrt{x - 41} + 3$

Step 1.4.3

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

$y - 3 = - \sqrt{x - 41}$

Step 1.4.4

Add $3$ to both sides of the equation.

$y = - \sqrt{x - 41} + 3$

Step 1.4.5

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

$y = \sqrt{x - 41} + 3$

$y = - \sqrt{x - 41} + 3$

$y = \sqrt{x - 41} + 3$

$y = - \sqrt{x - 41} + 3$

$y = \sqrt{x - 41} + 3$

$y = - \sqrt{x - 41} + 3$

Step 2

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$y = a x^{2} + b x + c$

Step 3

The standard form is $\sqrt{x - 41} + 3, - \sqrt{x - 41} + 3$ .

$y = \sqrt{x - 41} + 3$

$y = - \sqrt{x - 41} + 3$

Step 4