Solve for r r = square root of 18+7r

$r = \sqrt{18 + 7 r}$

Since the radical is on the right side of the equation, switch the sides so it is on the left side of the equation.

$\sqrt{18 + 7 r} = r$

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

${\sqrt{18 + 7 r}}^{2} = r^{2}$

Simplify each side of the equation.

Use $\sqrt[n]{a^{x}} = a^{\frac{x}{n}}$ to rewrite $\sqrt{18 + 7 r}$ as ${(18 + 7 r)}^{\frac{1}{2}}$ .

${({(18 + 7 r)}^{\frac{1}{2}})}^{2} = r^{2}$

Simplify the left side.

Simplify ${({(18 + 7 r)}^{\frac{1}{2}})}^{2}$ .

Multiply the exponents in ${({(18 + 7 r)}^{\frac{1}{2}})}^{2}$ .

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

${(18 + 7 r)}^{\frac{1}{2} \cdot 2} = r^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(18 + 7 r)}^{\frac{1}{2} \cdot 2} = r^{2}$

Rewrite the expression.

${(18 + 7 r)}^{1} = r^{2}$

Simplify.

$18 + 7 r = r^{2}$

Solve for $r$ .

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

$18 + 7 r - r^{2} = 0$

Factor the left side of the equation.

Factor $- 1$ out of $18 + 7 r - r^{2}$ .

Reorder the expression.

Move $18$ .

$7 r - r^{2} + 18 = 0$

Reorder $7 r$ and $- r^{2}$ .

$- r^{2} + 7 r + 18 = 0$

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

$- (r^{2}) + 7 r + 18 = 0$

Factor $- 1$ out of $7 r$ .

$- (r^{2}) - (- 7 r) + 18 = 0$

Rewrite $18$ as $- 1 (- 18)$ .

$- (r^{2}) - (- 7 r) - 1 \cdot - 18 = 0$

Factor $- 1$ out of $- (r^{2}) - (- 7 r)$ .

$- (r^{2} - 7 r) - 1 \cdot - 18 = 0$

Factor $- 1$ out of $- (r^{2} - 7 r) - 1 (- 18)$ .

$- (r^{2} - 7 r - 18) = 0$

Factor.

Factor $r^{2} - 7 r - 18$ 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 $- 18$ and whose sum is $- 7$ .

$- 9, 2$

Write the factored form using these integers.

$- ((r - 9) (r + 2)) = 0$

Remove unnecessary parentheses.

$- (r - 9) (r + 2) = 0$

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

$r - 9 = 0$

$r + 2 = 0$

Set $r - 9$ equal to $0$ and solve for $r$ .

Set $r - 9$ equal to $0$ .

$r - 9 = 0$

Add $9$ to both sides of the equation.

$r = 9$

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

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

$r + 2 = 0$

Subtract $2$ from both sides of the equation.

$r = - 2$

The final solution is all the values that make $- (r - 9) (r + 2) = 0$ true.

$r = 9, - 2$

Exclude the solutions that do not make $r = \sqrt{18 + 7 r}$ true.

$r = 9$

Solve for r r = square root of 18+7r

Related Questions

Support LCMGCF.com by disabling your adblocker.