Calculus Examples

$\sqrt{x} + 3 = 8$

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

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Since $3$ does not contain the variable to solve for, move it to the right side of the equation by subtracting $3$ from both sides.

$\sqrt{x} = - 3 + 8$

Add $- 3$ and $8$ to get $5$ .

$\sqrt{x} = 5$

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

${(\sqrt{x})}^{2} = {(5)}^{2}$

Simplify the left side of the equation.

$x = {(5)}^{2}$

Simplify the right side of the equation.

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Remove parentheses around $5$ .

$x = 5^{2}$

Raise $5$ to the power of $2$ to get $25$ .

$x = 25$

Verify each of the solutions by substituting them back into the original equation $\sqrt{x} + 3 = 8$ and solving. In this case, all solutions were found to be valid.

$x = 25$

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Calculus Examples

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