Pre-Algebra Examples

${(1.43 g)}^{2} + g^{2} = 1$

Step 1

Simplify ${(1.43 g)}^{2} + g^{2}$ .

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Step 1.1

Simplify each term.

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Step 1.1.1

Apply the product rule to $1.43 g$ .

${1.43}^{2} g^{2} + g^{2} = 1$

Step 1.1.2

Raise $1.43$ to the power of $2$ .

$2.0449 g^{2} + g^{2} = 1$

Step 1.2

Add $2.0449 g^{2}$ and $g^{2}$ .

$3.0449 g^{2} = 1$

Step 2

Divide each term in $3.0449 g^{2} = 1$ by $3.0449$ and simplify.

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Step 2.1

Divide each term in $3.0449 g^{2} = 1$ by $3.0449$ .

$\frac{3.0449 g^{2}}{3.0449} = \frac{1}{3.0449}$

Step 2.2

Simplify the left side.

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Step 2.2.1

Cancel the common factor of $3.0449$ .

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Step 2.2.1.1

Cancel the common factor.

$\frac{3.0449 g^{2}}{3.0449} = \frac{1}{3.0449}$

Step 2.2.1.2

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

$g^{2} = \frac{1}{3.0449}$

Step 2.3

Simplify the right side.

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Step 2.3.1

Divide $1$ by $3.0449$ .

$g^{2} = 0.32841801$

Step 3

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

$g = \pm \sqrt{0.32841801}$

Step 4

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

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Step 4.1

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

$g = \sqrt{0.32841801}$

Step 4.2

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

$g = - \sqrt{0.32841801}$

Step 4.3

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

$g = \sqrt{0.32841801}, - \sqrt{0.32841801}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$g = \sqrt{0.32841801}, - \sqrt{0.32841801}$

Decimal Form:

$g = 0.57307766 \dots, - 0.57307766 \dots$