Solve by Factoring (7x-3)^(1/2)=5

${(7 x - 3)}^{\frac{1}{2}} = 5$

Move $5$ to the left side of the equation by subtracting it from both sides.

${(7 x - 3)}^{\frac{1}{2}} - 5 = 0$

Add $5$ to both sides of the equation.

${(7 x - 3)}^{\frac{1}{2}} = 5$

Raise each side of the equation to the $2$ power to eliminate the fractional exponent on the left side.

${({(7 x - 3)}^{\frac{1}{2}})}^{2} = {(5)}^{2}$

Solve the equation for $x$ .

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

$7 x - 3 = 25$

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

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Add $3$ to both sides of the equation.

$7 x = 25 + 3$

Add $25$ and $3$ .

$7 x = 28$

Divide each term by $7$ and simplify.

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Divide each term in $7 x = 28$ by $7$ .

$\frac{7 x}{7} = \frac{28}{7}$

Cancel the common factor of $7$ .

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Cancel the common factor.

$\frac{7 x}{7} = \frac{28}{7}$

Divide $x$ by $1$ .

$x = \frac{28}{7}$

Divide $28$ by $7$ .

$x = 4$

Solve by Factoring (7x-3)^(1/2)=5

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