Trigonometry Examples

$(2 x^{2}) = (3 x^{2} - 64)$

Step 1

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

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Step 1.1

Subtract $3 x^{2}$ from both sides of the equation.

$2 x^{2} - 3 x^{2} = - 64$

Step 1.2

Subtract $3 x^{2}$ from $2 x^{2}$ .

$- x^{2} = - 64$

Step 2

Divide each term in $- x^{2} = - 64$ by $- 1$ and simplify.

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Step 2.1

Divide each term in $- x^{2} = - 64$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{- 64}{- 1}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{- 64}{- 1}$

Step 2.2.2

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

$x^{2} = \frac{- 64}{- 1}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $- 64$ by $- 1$ .

$x^{2} = 64$

Step 3

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

$x = \pm \sqrt{64}$

Step 4

Simplify $\pm \sqrt{64}$ .

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Step 4.1

Rewrite $64$ as $8^{2}$ .

$x = \pm \sqrt{8^{2}}$

Step 4.2

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

$x = \pm 8$

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.

$x = 8$

Step 5.2

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

$x = - 8$

Step 5.3

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

$x = 8, - 8$