Basic Math Examples

$y^{2} - 1 \frac{9}{16} = 0$

Step 1

Simplify the left side.

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Step 1.1

Convert $1 \frac{9}{16}$ to an improper fraction.

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Step 1.1.1

A mixed number is an addition of its whole and fractional parts.

$y^{2} - (1 + \frac{9}{16}) = 0$

Step 1.1.2

Add $1$ and $\frac{9}{16}$ .

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Step 1.1.2.1

Write $1$ as a fraction with a common denominator.

$y^{2} - (\frac{16}{16} + \frac{9}{16}) = 0$

Step 1.1.2.2

Combine the numerators over the common denominator.

$y^{2} - \frac{16 + 9}{16} = 0$

Step 1.1.2.3

Add $16$ and $9$ .

$y^{2} - \frac{25}{16} = 0$

Step 2

Add $\frac{25}{16}$ to both sides of the equation.

$y^{2} = \frac{25}{16}$

Step 3

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

$y = \pm \sqrt{\frac{25}{16}}$

Step 4

Simplify $\pm \sqrt{\frac{25}{16}}$ .

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Step 4.1

Rewrite $\sqrt{\frac{25}{16}}$ as $\frac{\sqrt{25}}{\sqrt{16}}$ .

$y = \pm \frac{\sqrt{25}}{\sqrt{16}}$

Step 4.2

Simplify the numerator.

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Step 4.2.1

Rewrite $25$ as $5^{2}$ .

$y = \pm \frac{\sqrt{5^{2}}}{\sqrt{16}}$

Step 4.2.2

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

$y = \pm \frac{5}{\sqrt{16}}$

Step 4.3

Simplify the denominator.

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Step 4.3.1

Rewrite $16$ as $4^{2}$ .

$y = \pm \frac{5}{\sqrt{4^{2}}}$

Step 4.3.2

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

$y = \pm \frac{5}{4}$

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.

$y = \frac{5}{4}$

Step 5.2

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

$y = - \frac{5}{4}$

Step 5.3

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

$y = \frac{5}{4}, - \frac{5}{4}$

Step 6

The result can be shown in multiple forms.

Exact Form:

$y = \frac{5}{4}, - \frac{5}{4}$

Decimal Form:

$y = 1.25, - 1.25$

Mixed Number Form:

$y = 1 \frac{1}{4}, - 1 \frac{1}{4}$