Solve for x square root of 2x-1 = square root of 1-2x

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

Step 1

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

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

Step 2

Simplify each side of the equation.

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

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

Simplify the left side.

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

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

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

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

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

Simplify the right side.

Rewrite ${\sqrt{1 - 2 x}}^{2}$ as $1 - 2 x$ .

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

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

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

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

Combine $\frac{1}{2}$ and $2$ .

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

Cancel the common factor of $2$ .

Cancel the common factor.

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

Rewrite the expression.

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

Simplify.

$2 x - 1 = 1 - 2 x$

Step 3

Solve for $x$ .

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

Add $2 x$ to both sides of the equation.

$2 x - 1 + 2 x = 1$

Add $2 x$ and $2 x$ .

$4 x - 1 = 1$

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

Add $1$ to both sides of the equation.

$4 x = 1 + 1$

Add $1$ and $1$ .

$4 x = 2$

Divide each term in $4 x = 2$ by $4$ and simplify.

Divide each term in $4 x = 2$ by $4$ .

$\frac{4 x}{4} = \frac{2}{4}$

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4 x}{4} = \frac{2}{4}$

Divide $x$ by $1$ .

$x = \frac{2}{4}$

Simplify the right side.

Cancel the common factor of $2$ and $4$ .

Factor $2$ out of $2$ .

$x = \frac{2 (1)}{4}$

Cancel the common factors.

Factor $2$ out of $4$ .

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Cancel the common factor.

$x = \frac{2 \cdot 1}{2 \cdot 2}$

Rewrite the expression.

$x = \frac{1}{2}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{1}{2}$

Decimal Form:

$x = 0.5$

Solve for x square root of 2x-1 = square root of 1-2x

Related Questions

Support LCMGCF.com by disabling your adblocker.