Algebra Examples

$43 = 40 + \sqrt{0.001 x + 1}$

Step 1

Rewrite the equation as $40 + \sqrt{0.001 x + 1} = 43$ .

$40 + \sqrt{0.001 x + 1} = 43$

Step 2

Move all terms not containing $\sqrt{0.001 x + 1}$ to the right side of the equation.

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Step 2.1

Subtract $40$ from both sides of the equation.

$\sqrt{0.001 x + 1} = 43 - 40$

Step 2.2

Subtract $40$ from $43$ .

$\sqrt{0.001 x + 1} = 3$

Step 3

To remove the radical on the left side of the equation, square both sides of the equation.

${\sqrt{0.001 x + 1}}^{2} = 3^{2}$

Step 4

Simplify each side of the equation.

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Step 4.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{0.001 x + 1}$ as ${(0.001 x + 1)}^{\frac{1}{2}}$ .

${({(0.001 x + 1)}^{\frac{1}{2}})}^{2} = 3^{2}$

Step 4.2

Simplify the left side.

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Step 4.2.1

Simplify ${({(0.001 x + 1)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

Multiply the exponents in ${({(0.001 x + 1)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1.1

Apply the power rule and multiply exponents, ${(a^{m})}^{n} = a^{m n}$ .

${(0.001 x + 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 4.2.1.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.1.2.1

Cancel the common factor.

${(0.001 x + 1)}^{\frac{1}{2} \cdot 2} = 3^{2}$

Step 4.2.1.1.2.2

Rewrite the expression.

${(0.001 x + 1)}^{1} = 3^{2}$

Step 4.2.1.2

Simplify.

$0.001 x + 1 = 3^{2}$

Step 4.3

Simplify the right side.

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Step 4.3.1

Raise $3$ to the power of $2$ .

$0.001 x + 1 = 9$

Step 5

Solve for $x$ .

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Step 5.1

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

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Step 5.1.1

Subtract $1$ from both sides of the equation.

$0.001 x = 9 - 1$

Step 5.1.2

Subtract $1$ from $9$ .

$0.001 x = 8$

Step 5.2

Divide each term in $0.001 x = 8$ by $0.001$ and simplify.

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Step 5.2.1

Divide each term in $0.001 x = 8$ by $0.001$ .

$\frac{0.001 x}{0.001} = \frac{8}{0.001}$

Step 5.2.2

Simplify the left side.

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Step 5.2.2.1

Cancel the common factor of $0.001$ .

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Step 5.2.2.1.1

Cancel the common factor.

$\frac{0.001 x}{0.001} = \frac{8}{0.001}$

Step 5.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{8}{0.001}$

Step 5.2.3

Simplify the right side.

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Step 5.2.3.1

Divide $8$ by $0.001$ .

$x = 8000$