Solve for a square root of 7a-10- square root of 2a+5=0

$\sqrt{7 a - 10} - \sqrt{2 a + 5} = 0$

Step 1

Add $\sqrt{2 a + 5}$ to both sides of the equation.

$\sqrt{7 a - 10} = \sqrt{2 a + 5}$

Step 2

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

${\sqrt{7 a - 10}}^{2} = {\sqrt{2 a + 5}}^{2}$

Step 3

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{7 a - 10}$ as ${(7 a - 10)}^{\frac{1}{2}}$ .

${({(7 a - 10)}^{\frac{1}{2}})}^{2} = {\sqrt{2 a + 5}}^{2}$

Simplify the left side.

Simplify ${({(7 a - 10)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(7 a - 10)}^{\frac{1}{2}})}^{2}$ .

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

${(7 a - 10)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 a + 5}}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(7 a - 10)}^{\frac{1}{2} \cdot 2} = {\sqrt{2 a + 5}}^{2}$

Rewrite the expression.

${(7 a - 10)}^{1} = {\sqrt{2 a + 5}}^{2}$

Simplify.

$7 a - 10 = {\sqrt{2 a + 5}}^{2}$

Simplify the right side.

Rewrite ${\sqrt{2 a + 5}}^{2}$ as $2 a + 5$ .

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

$7 a - 10 = {({(2 a + 5)}^{\frac{1}{2}})}^{2}$

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

$7 a - 10 = {(2 a + 5)}^{\frac{1}{2} \cdot 2}$

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

$7 a - 10 = {(2 a + 5)}^{\frac{2}{2}}$

Cancel the common factor of $2$ .

Cancel the common factor.

$7 a - 10 = {(2 a + 5)}^{\frac{2}{2}}$

Rewrite the expression.

$7 a - 10 = {(2 a + 5)}^{1}$

Simplify.

$7 a - 10 = 2 a + 5$

Step 4

Solve for $a$ .

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

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

$7 a - 10 - 2 a = 5$

Subtract $2 a$ from $7 a$ .

$5 a - 10 = 5$

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

Add $10$ to both sides of the equation.

$5 a = 5 + 10$

Add $5$ and $10$ .

$5 a = 15$

Divide each term in $5 a = 15$ by $5$ and simplify.

Divide each term in $5 a = 15$ by $5$ .

$\frac{5 a}{5} = \frac{15}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 a}{5} = \frac{15}{5}$

Divide $a$ by $1$ .

$a = \frac{15}{5}$

Simplify the right side.

Divide $15$ by $5$ .

$a = 3$

Solve for a square root of 7a-10- square root of 2a+5=0

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