Solve by Factoring square root of 5x-1 = square root of 4x+9

$\sqrt{5 x - 1} = \sqrt{4 x + 9}$

Step 1

Subtract $\sqrt{4 x + 9}$ from both sides of the equation.

$\sqrt{5 x - 1} - \sqrt{4 x + 9} = 0$

Step 2

Add $\sqrt{4 x + 9}$ to both sides of the equation.

$\sqrt{5 x - 1} = \sqrt{4 x + 9}$

Step 3

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

${\sqrt{5 x - 1}}^{2} = {\sqrt{4 x + 9}}^{2}$

Step 4

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{5 x - 1}$ as ${(5 x - 1)}^{\frac{1}{2}}$ .

${({(5 x - 1)}^{\frac{1}{2}})}^{2} = {\sqrt{4 x + 9}}^{2}$

Simplify the left side.

Simplify ${({(5 x - 1)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(5 x - 1)}^{\frac{1}{2}})}^{2}$ .

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

${(5 x - 1)}^{\frac{1}{2} \cdot 2} = {\sqrt{4 x + 9}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x - 1)}^{\frac{1}{2} \cdot 2} = {\sqrt{4 x + 9}}^{2}$

Rewrite the expression.

${(5 x - 1)}^{1} = {\sqrt{4 x + 9}}^{2}$

Simplify.

$5 x - 1 = {\sqrt{4 x + 9}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{4 x + 9}}^{2}$ as $4 x + 9$ .

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{4 x + 9}$ as ${(4 x + 9)}^{\frac{1}{2}}$ .

$5 x - 1 = {({(4 x + 9)}^{\frac{1}{2}})}^{2}$

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

$5 x - 1 = {(4 x + 9)}^{\frac{1}{2} \cdot 2}$

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

$5 x - 1 = {(4 x + 9)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$5 x - 1 = {(4 x + 9)}^{\frac{2}{2}}$

Rewrite the expression.

$5 x - 1 = {(4 x + 9)}^{1}$

Simplify.

$5 x - 1 = 4 x + 9$

Step 5

Solve for $x$ .

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

Subtract $4 x$ from both sides of the equation.

$5 x - 1 - 4 x = 9$

Subtract $4 x$ from $5 x$ .

$x - 1 = 9$

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

Add $1$ to both sides of the equation.

$x = 9 + 1$

Add $9$ and $1$ .

$x = 10$

Solve by Factoring square root of 5x-1 = square root of 4x+9

Related Questions

Support LCMGCF.com by disabling your adblocker.