Solve for s square root of 3s+10=s

$\sqrt{3 s + 10} = s$

Step 1

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

${\sqrt{3 s + 10}}^{2} = s^{2}$

Step 2

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{3 s + 10}$ as ${(3 s + 10)}^{\frac{1}{2}}$ .

${({(3 s + 10)}^{\frac{1}{2}})}^{2} = s^{2}$

Simplify the left side.

Simplify ${({(3 s + 10)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(3 s + 10)}^{\frac{1}{2}})}^{2}$ .

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

${(3 s + 10)}^{\frac{1}{2} \cdot 2} = s^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(3 s + 10)}^{\frac{1}{2} \cdot 2} = s^{2}$

Rewrite the expression.

${(3 s + 10)}^{1} = s^{2}$

Simplify.

$3 s + 10 = s^{2}$

Step 3

Solve for $s$ .

Subtract $s^{2}$ from both sides of the equation.

$3 s + 10 - s^{2} = 0$

Factor the left side of the equation.

Factor $- 1$ out of $3 s + 10 - s^{2}$ .

Reorder the expression.

Move $10$ .

$3 s - s^{2} + 10 = 0$

Reorder $3 s$ and $- s^{2}$ .

$- s^{2} + 3 s + 10 = 0$

Factor $- 1$ out of $- s^{2}$ .

$- (s^{2}) + 3 s + 10 = 0$

Factor $- 1$ out of $3 s$ .

$- (s^{2}) - (- 3 s) + 10 = 0$

Rewrite $10$ as $- 1 (- 10)$ .

$- (s^{2}) - (- 3 s) - 1 \cdot - 10 = 0$

Factor $- 1$ out of $- (s^{2}) - (- 3 s)$ .

$- (s^{2} - 3 s) - 1 \cdot - 10 = 0$

Factor $- 1$ out of $- (s^{2} - 3 s) - 1 (- 10)$ .

$- (s^{2} - 3 s - 10) = 0$

Factor.

Factor $s^{2} - 3 s - 10$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 10$ and whose sum is $- 3$ .

$- 5, 2$

Write the factored form using these integers.

$- ((s - 5) (s + 2)) = 0$

Remove unnecessary parentheses.

$- (s - 5) (s + 2) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$s - 5 = 0$

$s + 2 = 0$

Set $s - 5$ equal to $0$ and solve for $s$ .

Set $s - 5$ equal to $0$ .

$s - 5 = 0$

Add $5$ to both sides of the equation.

$s = 5$

Set $s + 2$ equal to $0$ and solve for $s$ .

Set $s + 2$ equal to $0$ .

$s + 2 = 0$

Subtract $2$ from both sides of the equation.

$s = - 2$

The final solution is all the values that make $- (s - 5) (s + 2) = 0$ true.

$s = 5, - 2$

Step 4

Exclude the solutions that do not make $\sqrt{3 s + 10} = s$ true.

$s = 5$

Solve for s square root of 3s+10=s

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