Solve for x square root of 3x-7+ square root of 2x-1=0

$\sqrt{3 x - 7} + \sqrt{2 x - 1} = 0$

Step 1

Subtract $\sqrt{2 x - 1}$ from both sides of the equation.

$\sqrt{3 x - 7} = - \sqrt{2 x - 1}$

Step 2

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

${\sqrt{3 x - 7}}^{2} = {(- \sqrt{2 x - 1})}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 x - 7}$ as ${(3 x - 7)}^{\frac{1}{2}}$ .

${({(3 x - 7)}^{\frac{1}{2}})}^{2} = {(- \sqrt{2 x - 1})}^{2}$

Simplify the left side.

Simplify ${({(3 x - 7)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 x - 7)}^{\frac{1}{2}})}^{2}$ .

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

${(3 x - 7)}^{\frac{1}{2} \cdot 2} = {(- \sqrt{2 x - 1})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 x - 7)}^{\frac{1}{2} \cdot 2} = {(- \sqrt{2 x - 1})}^{2}$

Rewrite the expression.

${(3 x - 7)}^{1} = {(- \sqrt{2 x - 1})}^{2}$

Simplify.

$3 x - 7 = {(- \sqrt{2 x - 1})}^{2}$

Simplify the right side.

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

Simplify the expression.

Apply the product rule to $- \sqrt{2 x - 1}$ .

$3 x - 7 = {(- 1)}^{2} {\sqrt{2 x - 1}}^{2}$

Raise $- 1$ to the power of $2$ .

$3 x - 7 = 1 {\sqrt{2 x - 1}}^{2}$

Multiply ${\sqrt{2 x - 1}}^{2}$ by $1$ .

$3 x - 7 = {\sqrt{2 x - 1}}^{2}$

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

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

$3 x - 7 = {({(2 x - 1)}^{\frac{1}{2}})}^{2}$

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

$3 x - 7 = {(2 x - 1)}^{\frac{1}{2} \cdot 2}$

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

$3 x - 7 = {(2 x - 1)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$3 x - 7 = {(2 x - 1)}^{\frac{2}{2}}$

Rewrite the expression.

$3 x - 7 = {(2 x - 1)}^{1}$

Simplify.

$3 x - 7 = 2 x - 1$

Step 4

Solve for $x$ .

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

Subtract $2 x$ from both sides of the equation.

$3 x - 7 - 2 x = - 1$

Subtract $2 x$ from $3 x$ .

$x - 7 = - 1$

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

Add $7$ to both sides of the equation.

$x = - 1 + 7$

Add $- 1$ and $7$ .

$x = 6$

Step 5

Exclude the solutions that do not make $\sqrt{3 x - 7} + \sqrt{2 x - 1} = 0$ true.

$No solution$

Solve for x square root of 3x-7+ square root of 2x-1=0

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