Solve by Factoring 4(x-3)^(1/2)=8

$4 {(x - 3)}^{\frac{1}{2}} = 8$

Move $8$ to the left side of the equation by subtracting it from both sides.

$4 {(x - 3)}^{\frac{1}{2}} - 8 = 0$

Factor $4$ out of $4 {(x - 3)}^{\frac{1}{2}} - 8$ .

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Factor $4$ out of $4 {(x - 3)}^{\frac{1}{2}}$ .

$4 ({(x - 3)}^{\frac{1}{2}}) - 8 = 0$

Factor $4$ out of $- 8$ .

$4 {(x - 3)}^{\frac{1}{2}} + 4 \cdot - 2 = 0$

Factor $4$ out of $4 {(x - 3)}^{\frac{1}{2}} + 4 \cdot - 2$ .

$4 ({(x - 3)}^{\frac{1}{2}} - 2) = 0$

Simplify.

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Apply the distributive property.

$4 {(x - 3)}^{\frac{1}{2}} + 4 \cdot - 2 = 0$

Multiply $4$ by $- 2$ .

$4 {(x - 3)}^{\frac{1}{2}} - 8 = 0$

Divide each term by $4$ and simplify.

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Divide each term in $4 {(x - 3)}^{\frac{1}{2}} - 8 = 0$ by $4$ .

$\frac{4 {(x - 3)}^{\frac{1}{2}} - 8}{4} = \frac{0}{4}$

Simplify $\frac{4 {(x - 3)}^{\frac{1}{2}} - 8}{4}$ .

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Factor $4$ out of $4 {(x - 3)}^{\frac{1}{2}}$ .

$\frac{4 ({(x - 3)}^{\frac{1}{2}}) - 8}{4} = \frac{0}{4}$

Factor $4$ out of $- 8$ .

$\frac{4 ({(x - 3)}^{\frac{1}{2}}) + 4 \cdot - 2}{4} = \frac{0}{4}$

Factor $4$ out of $4 ({(x - 3)}^{\frac{1}{2}}) + 4 (- 2)$ .

$\frac{4 ({(x - 3)}^{\frac{1}{2}} - 2)}{4} = \frac{0}{4}$

Cancel the common factors.

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Factor $4$ out of $4$ .

$\frac{4 ({(x - 3)}^{\frac{1}{2}} - 2)}{4 (1)} = \frac{0}{4}$

Cancel the common factor.

$\frac{4 ({(x - 3)}^{\frac{1}{2}} - 2)}{4 \cdot 1} = \frac{0}{4}$

Rewrite the expression.

$\frac{{(x - 3)}^{\frac{1}{2}} - 2}{1} = \frac{0}{4}$

Divide ${(x - 3)}^{\frac{1}{2}} - 2$ by $1$ .

${(x - 3)}^{\frac{1}{2}} - 2 = \frac{0}{4}$

Divide $0$ by $4$ .

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

Add $2$ to both sides of the equation.

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

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

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

Solve the equation for $x$ .

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

$x - 3 = 4$

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.

$x = 4 + 3$

Add $4$ and $3$ .

$x = 7$

Solve by Factoring 4(x-3)^(1/2)=8

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