Basic Math Examples

$5 y^{2} - 25 = 4 y^{2} + 24$

Step 1

Move all terms containing $y$ to the left side of the equation.

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Step 1.1

Subtract $4 y^{2}$ from both sides of the equation.

$5 y^{2} - 25 - 4 y^{2} = 24$

Step 1.2

Subtract $4 y^{2}$ from $5 y^{2}$ .

$y^{2} - 25 = 24$

Step 2

Move all terms not containing $y$ to the right side of the equation.

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Step 2.1

Add $25$ to both sides of the equation.

$y^{2} = 24 + 25$

Step 2.2

Add $24$ and $25$ .

$y^{2} = 49$

Step 3

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

$y = \pm \sqrt{49}$

Step 4

Simplify $\pm \sqrt{49}$ .

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Step 4.1

Rewrite $49$ as $7^{2}$ .

$y = \pm \sqrt{7^{2}}$

Step 4.2

Pull terms out from under the radical, assuming positive real numbers.

$y = \pm 7$

Step 5

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

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Step 5.1

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

$y = 7$

Step 5.2

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

$y = - 7$

Step 5.3

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

$y = 7, - 7$