Trigonometry Examples

$x^{2} + 24 \cdot 24 = 25 x^{2}$

Step 1

Multiply $24$ by $24$ .

$x^{2} + 576 = 25 x^{2}$

Step 2

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

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Step 2.1

Subtract $25 x^{2}$ from both sides of the equation.

$x^{2} + 576 - 25 x^{2} = 0$

Step 2.2

Subtract $25 x^{2}$ from $x^{2}$ .

$- 24 x^{2} + 576 = 0$

Step 3

Subtract $576$ from both sides of the equation.

$- 24 x^{2} = - 576$

Step 4

Divide each term in $- 24 x^{2} = - 576$ by $- 24$ and simplify.

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Step 4.1

Divide each term in $- 24 x^{2} = - 576$ by $- 24$ .

$\frac{- 24 x^{2}}{- 24} = \frac{- 576}{- 24}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Cancel the common factor of $- 24$ .

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Step 4.2.1.1

Cancel the common factor.

$\frac{- 24 x^{2}}{- 24} = \frac{- 576}{- 24}$

Step 4.2.1.2

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{- 576}{- 24}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Divide $- 576$ by $- 24$ .

$x^{2} = 24$

Step 5

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

$x = \pm \sqrt{24}$

Step 6

Simplify $\pm \sqrt{24}$ .

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Step 6.1

Rewrite $24$ as $2^{2} \cdot 6$ .

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Step 6.1.1

Factor $4$ out of $24$ .

$x = \pm \sqrt{4 (6)}$

Step 6.1.2

Rewrite $4$ as $2^{2}$ .

$x = \pm \sqrt{2^{2} \cdot 6}$

Step 6.2

Pull terms out from under the radical.

$x = \pm 2 \sqrt{6}$

Step 7

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

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Step 7.1

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

$x = 2 \sqrt{6}$

Step 7.2

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

$x = - 2 \sqrt{6}$

Step 7.3

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

$x = 2 \sqrt{6}, - 2 \sqrt{6}$

Step 8

The result can be shown in multiple forms.

Exact Form:

$x = 2 \sqrt{6}, - 2 \sqrt{6}$

Decimal Form:

$x = 4.89897948 \dots, - 4.89897948 \dots$