Solve for x square root of 8x+3=2 square root of 7x-3

$\sqrt{8 x + 3} = 2 \sqrt{7 x - 3}$

Step 1

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

${\sqrt{8 x + 3}}^{2} = {(2 \sqrt{7 x - 3})}^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{8 x + 3}$ as ${(8 x + 3)}^{\frac{1}{2}}$ .

${({(8 x + 3)}^{\frac{1}{2}})}^{2} = {(2 \sqrt{7 x - 3})}^{2}$

Simplify the left side.

Simplify ${({(8 x + 3)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(8 x + 3)}^{\frac{1}{2}})}^{2}$ .

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

${(8 x + 3)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{7 x - 3})}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(8 x + 3)}^{\frac{1}{2} \cdot 2} = {(2 \sqrt{7 x - 3})}^{2}$

Rewrite the expression.

${(8 x + 3)}^{1} = {(2 \sqrt{7 x - 3})}^{2}$

Simplify.

$8 x + 3 = {(2 \sqrt{7 x - 3})}^{2}$

Simplify the right side.

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

Simplify the expression.

Apply the product rule to $2 \sqrt{7 x - 3}$ .

$8 x + 3 = 2^{2} {\sqrt{7 x - 3}}^{2}$

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

$8 x + 3 = 4 {\sqrt{7 x - 3}}^{2}$

Rewrite ${\sqrt{7 x - 3}}^{2}$ as $7 x - 3$ .

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

$8 x + 3 = 4 {({(7 x - 3)}^{\frac{1}{2}})}^{2}$

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

$8 x + 3 = 4 {(7 x - 3)}^{\frac{1}{2} \cdot 2}$

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

$8 x + 3 = 4 {(7 x - 3)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$8 x + 3 = 4 {(7 x - 3)}^{\frac{2}{2}}$

Rewrite the expression.

$8 x + 3 = 4 {(7 x - 3)}^{1}$

Simplify.

$8 x + 3 = 4 (7 x - 3)$

Apply the distributive property.

$8 x + 3 = 4 (7 x) + 4 \cdot - 3$

Multiply.

Multiply $7$ by $4$ .

$8 x + 3 = 28 x + 4 \cdot - 3$

Multiply $4$ by $- 3$ .

$8 x + 3 = 28 x - 12$

Step 3

Solve for $x$ .

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

Subtract $28 x$ from both sides of the equation.

$8 x + 3 - 28 x = - 12$

Subtract $28 x$ from $8 x$ .

$- 20 x + 3 = - 12$

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

Subtract $3$ from both sides of the equation.

$- 20 x = - 12 - 3$

Subtract $3$ from $- 12$ .

$- 20 x = - 15$

Divide each term in $- 20 x = - 15$ by $- 20$ and simplify.

Divide each term in $- 20 x = - 15$ by $- 20$ .

$\frac{- 20 x}{- 20} = \frac{- 15}{- 20}$

Simplify the left side.

Cancel the common factor of $- 20$ .

Cancel the common factor.

$\frac{- 20 x}{- 20} = \frac{- 15}{- 20}$

Divide $x$ by $1$ .

$x = \frac{- 15}{- 20}$

Simplify the right side.

Cancel the common factor of $- 15$ and $- 20$ .

Factor $- 5$ out of $- 15$ .

$x = \frac{- 5 (3)}{- 20}$

Cancel the common factors.

Factor $- 5$ out of $- 20$ .

$x = \frac{- 5 \cdot 3}{- 5 \cdot 4}$

Cancel the common factor.

$x = \frac{- 5 \cdot 3}{- 5 \cdot 4}$

Rewrite the expression.

$x = \frac{3}{4}$

Step 4

The result can be shown in multiple forms.

Exact Form:

$x = \frac{3}{4}$

Decimal Form:

$x = 0.75$

Solve for x square root of 8x+3=2 square root of 7x-3

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