Algebra Examples

$12 + \sqrt{2 x - 1} = 4$

Step 1

Move all terms not containing $\sqrt{2 x - 1}$ to the right side of the equation.

Tap for more steps...

Step 1.1

Subtract $12$ from both sides of the equation.

$\sqrt{2 x - 1} = 4 - 12$

Step 1.2

Subtract $12$ from $4$ .

$\sqrt{2 x - 1} = - 8$

Step 2

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

${\sqrt{2 x - 1}}^{2} = {(- 8)}^{2}$

Step 3

Simplify each side of the equation.

Tap for more steps...

Step 3.1

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{2 x - 1}$ as ${(2 x - 1)}^{\frac{1}{2}}$ .

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

Step 3.2

Simplify the left side.

Tap for more steps...

Step 3.2.1

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

Tap for more steps...

Step 3.2.1.1

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

Tap for more steps...

Step 3.2.1.1.1

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

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

Step 3.2.1.1.2

Cancel the common factor of $2$ .

Tap for more steps...

Step 3.2.1.1.2.1

Cancel the common factor.

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

Step 3.2.1.1.2.2

Rewrite the expression.

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

Step 3.2.1.2

Simplify.

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

Step 3.3

Simplify the right side.

Tap for more steps...

Step 3.3.1

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

$2 x - 1 = 64$

Step 4

Solve for $x$ .

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Add $1$ to both sides of the equation.

$2 x = 64 + 1$

Step 4.1.2

Add $64$ and $1$ .

$2 x = 65$

Step 4.2

Divide each term in $2 x = 65$ by $2$ and simplify.

Tap for more steps...

Step 4.2.1

Divide each term in $2 x = 65$ by $2$ .

$\frac{2 x}{2} = \frac{65}{2}$

Step 4.2.2

Simplify the left side.

Tap for more steps...

Step 4.2.2.1

Cancel the common factor of $2$ .

Tap for more steps...

Step 4.2.2.1.1

Cancel the common factor.

$\frac{2 x}{2} = \frac{65}{2}$

Step 4.2.2.1.2

Divide $x$ by $1$ .

$x = \frac{65}{2}$

Step 5

Exclude the solutions that do not make $12 + \sqrt{2 x - 1} = 4$ true.

$No solution$