Trigonometry Examples

$4 x^{2} + 1 = 37$

Step 1

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

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Step 1.1

Subtract $1$ from both sides of the equation.

$4 x^{2} = 37 - 1$

Step 1.2

Subtract $1$ from $37$ .

$4 x^{2} = 36$

Step 2

Divide each term in $4 x^{2} = 36$ by $4$ and simplify.

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Step 2.1

Divide each term in $4 x^{2} = 36$ by $4$ .

$\frac{4 x^{2}}{4} = \frac{36}{4}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $4$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{4 x^{2}}{4} = \frac{36}{4}$

Step 2.2.1.2

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

$x^{2} = \frac{36}{4}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $36$ by $4$ .

$x^{2} = 9$

Step 3

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

$x = \pm \sqrt{9}$

Step 4

Simplify $\pm \sqrt{9}$ .

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Step 4.1

Rewrite $9$ as $3^{2}$ .

$x = \pm \sqrt{3^{2}}$

Step 4.2

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

$x = \pm 3$

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.

$x = 3$

Step 5.2

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

$x = - 3$

Step 5.3

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

$x = 3, - 3$