Algebra Examples

$2 {(x - 1)}^{\frac{1}{2}} = {(26 + x)}^{\frac{1}{2}}$

Step 1

Divide each term in $2 {(x - 1)}^{\frac{1}{2}} = {(26 + x)}^{\frac{1}{2}}$ by $2$ and simplify.

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Step 1.1

Divide each term in $2 {(x - 1)}^{\frac{1}{2}} = {(26 + x)}^{\frac{1}{2}}$ by $2$ .

$\frac{2 {(x - 1)}^{\frac{1}{2}}}{2} = \frac{{(26 + x)}^{\frac{1}{2}}}{2}$

Step 1.2

Simplify the left side.

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Step 1.2.1

Cancel the common factor.

$\frac{2 {(x - 1)}^{\frac{1}{2}}}{2} = \frac{{(26 + x)}^{\frac{1}{2}}}{2}$

Step 1.2.2

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

${(x - 1)}^{\frac{1}{2}} = \frac{{(26 + x)}^{\frac{1}{2}}}{2}$

Step 2

Eliminate the fractional exponents by multiplying both exponents by the LCD.

${({(x - 1)}^{\frac{1}{2}})}^{2} = {(\frac{{(26 + x)}^{\frac{1}{2}}}{2})}^{2}$

Step 3

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

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Step 3.1

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

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Step 3.1.1

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

${(x - 1)}^{\frac{1}{2} \cdot 2} = {(\frac{{(26 + x)}^{\frac{1}{2}}}{2})}^{2}$

Step 3.1.2

Cancel the common factor of $2$ .

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Step 3.1.2.1

Cancel the common factor.

${(x - 1)}^{\frac{1}{2} \cdot 2} = {(\frac{{(26 + x)}^{\frac{1}{2}}}{2})}^{2}$

Step 3.1.2.2

Rewrite the expression.

${(x - 1)}^{1} = {(\frac{{(26 + x)}^{\frac{1}{2}}}{2})}^{2}$

Step 3.2

Simplify.

$x - 1 = {(\frac{{(26 + x)}^{\frac{1}{2}}}{2})}^{2}$

Step 4

Simplify ${(\frac{{(26 + x)}^{\frac{1}{2}}}{2})}^{2}$ .

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Step 4.1

Apply the product rule to $\frac{{(26 + x)}^{\frac{1}{2}}}{2}$ .

$x - 1 = \frac{{({(26 + x)}^{\frac{1}{2}})}^{2}}{2^{2}}$

Step 4.2

Simplify the numerator.

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Step 4.2.1

Multiply the exponents in ${({(26 + x)}^{\frac{1}{2}})}^{2}$ .

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Step 4.2.1.1

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

$x - 1 = \frac{{(26 + x)}^{\frac{1}{2} \cdot 2}}{2^{2}}$

Step 4.2.1.2

Cancel the common factor of $2$ .

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Step 4.2.1.2.1

Cancel the common factor.

$x - 1 = \frac{{(26 + x)}^{\frac{1}{2} \cdot 2}}{2^{2}}$

Step 4.2.1.2.2

Rewrite the expression.

$x - 1 = \frac{{(26 + x)}^{1}}{2^{2}}$

Step 4.2.2

Simplify.

$x - 1 = \frac{26 + x}{2^{2}}$

Step 4.3

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

$x - 1 = \frac{26 + x}{4}$

Step 5

Multiply both sides by $4$ .

$(x - 1) \cdot 4 = \frac{26 + x}{4} \cdot 4$

Step 6

Simplify.

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Step 6.1

Simplify the left side.

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Step 6.1.1

Simplify $(x - 1) \cdot 4$ .

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Step 6.1.1.1

Apply the distributive property.

$x \cdot 4 - 1 \cdot 4 = \frac{26 + x}{4} \cdot 4$

Step 6.1.1.2

Simplify the expression.

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Step 6.1.1.2.1

Move $4$ to the left of $x$ .

$4 \cdot x - 1 \cdot 4 = \frac{26 + x}{4} \cdot 4$

Step 6.1.1.2.2

Multiply $- 1$ by $4$ .

$4 x - 4 = \frac{26 + x}{4} \cdot 4$

Step 6.2

Simplify the right side.

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Step 6.2.1

Simplify $\frac{26 + x}{4} \cdot 4$ .

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Step 6.2.1.1

Cancel the common factor of $4$ .

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Step 6.2.1.1.1

Cancel the common factor.

$4 x - 4 = \frac{26 + x}{4} \cdot 4$

Step 6.2.1.1.2

Rewrite the expression.

$4 x - 4 = 26 + x$

Step 6.2.1.2

Reorder $26$ and $x$ .

$4 x - 4 = x + 26$

Step 7

Solve for $x$ .

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Step 7.1

Move all terms containing $x$ to the left side of the equation.

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Step 7.1.1

Subtract $x$ from both sides of the equation.

$4 x - 4 - x = 26$

Step 7.1.2

Subtract $x$ from $4 x$ .

$3 x - 4 = 26$

Step 7.2

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

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Step 7.2.1

Add $4$ to both sides of the equation.

$3 x = 26 + 4$

Step 7.2.2

Add $26$ and $4$ .

$3 x = 30$

Step 7.3

Divide each term in $3 x = 30$ by $3$ and simplify.

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Step 7.3.1

Divide each term in $3 x = 30$ by $3$ .

$\frac{3 x}{3} = \frac{30}{3}$

Step 7.3.2

Simplify the left side.

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Step 7.3.2.1

Cancel the common factor of $3$ .

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Step 7.3.2.1.1

Cancel the common factor.

$\frac{3 x}{3} = \frac{30}{3}$

Step 7.3.2.1.2

Divide $x$ by $1$ .

$x = \frac{30}{3}$

Step 7.3.3

Simplify the right side.

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Step 7.3.3.1

Divide $30$ by $3$ .

$x = 10$