Algebra Examples

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

Step 1

Subtract $8$ from both sides of the equation.

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

Step 2

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

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Step 2.1

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

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

Step 2.2

Factor $4$ out of $- 8$ .

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

Step 2.3

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

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

Step 3

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

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Step 3.1

Apply the distributive property.

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

Step 3.2

Multiply $4$ by $- 2$ .

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

Step 4

Add $8$ to both sides of the equation.

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

Step 5

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

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

Step 6

Simplify the exponent.

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Step 6.1

Simplify the left side.

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Step 6.1.1

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

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Step 6.1.1.1

Apply the product rule to $4 {(x - 3)}^{\frac{1}{2}}$ .

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

Step 6.1.1.2

Raise $4$ to the power of $2$ .

$16 {({(x - 3)}^{\frac{1}{2}})}^{2} = 8^{2}$

Step 6.1.1.3

Multiply the exponents in ${({(x - 3)}^{\frac{1}{2}})}^{2}$ .

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Step 6.1.1.3.1

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

$16 {(x - 3)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Step 6.1.1.3.2

Cancel the common factor of $2$ .

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Step 6.1.1.3.2.1

Cancel the common factor.

$16 {(x - 3)}^{\frac{1}{2} \cdot 2} = 8^{2}$

Step 6.1.1.3.2.2

Rewrite the expression.

$16 {(x - 3)}^{1} = 8^{2}$

Step 6.1.1.4

Simplify.

$16 (x - 3) = 8^{2}$

Step 6.1.1.5

Apply the distributive property.

$16 x + 16 \cdot - 3 = 8^{2}$

Step 6.1.1.6

Multiply $16$ by $- 3$ .

$16 x - 48 = 8^{2}$

Step 6.2

Simplify the right side.

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Step 6.2.1

Raise $8$ to the power of $2$ .

$16 x - 48 = 64$

Step 7

Solve for $x$ .

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Step 7.1

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

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Step 7.1.1

Add $48$ to both sides of the equation.

$16 x = 64 + 48$

Step 7.1.2

Add $64$ and $48$ .

$16 x = 112$

Step 7.2

Divide each term in $16 x = 112$ by $16$ and simplify.

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Step 7.2.1

Divide each term in $16 x = 112$ by $16$ .

$\frac{16 x}{16} = \frac{112}{16}$

Step 7.2.2

Simplify the left side.

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Step 7.2.2.1

Cancel the common factor of $16$ .

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Step 7.2.2.1.1

Cancel the common factor.

$\frac{16 x}{16} = \frac{112}{16}$

Step 7.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{112}{16}$

Step 7.2.3

Simplify the right side.

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Step 7.2.3.1

Divide $112$ by $16$ .

$x = 7$