Precalculus Examples

$\sqrt{x} + 5 = 6$

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

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Subtract $5$ from both sides of the equation.

$\sqrt{x} = 6 - 5$

Subtract $5$ from $6$ .

$\sqrt{x} = 1$

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

${\sqrt{x}}^{2} = 1^{2}$

Simplify each side of the equation.

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

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

$x^{\frac{1}{2} \cdot 2} = 1^{2}$

Cancel the common factor of $2$ .

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Cancel the common factor.

$x^{\frac{1}{2} \cdot 2} = 1^{2}$

Rewrite the expression.

$x^{1} = 1^{2}$

Simplify.

$x = 1^{2}$

One to any power is one.

$x = 1$

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