Solve for h 18+7h^(1/2)=12

$18 + 7 h^{\frac{1}{2}} = 12$

Step 1

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

Subtract $18$ from both sides of the equation.

$7 h^{\frac{1}{2}} - 12 = - 18$

Add $12$ to both sides of the equation.

$7 h^{\frac{1}{2}} = - 18 + 12$

Add $- 18$ and $12$ .

$7 h^{\frac{1}{2}} = - 6$

Step 2

Raise each side of the equation to the power of $2$ to eliminate the fractional exponent on the left side.

${(7 h^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Step 3

Simplify the exponent.

Simplify the left side.

Simplify ${(7 h^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $7 h^{\frac{1}{2}}$ .

$7^{2} {(h^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Raise $7$ to the power of $2$ .

$49 {(h^{\frac{1}{2}})}^{2} = {(- 6)}^{2}$

Multiply the exponents in ${(h^{\frac{1}{2}})}^{2}$ .

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

$49 h^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$49 h^{\frac{1}{2} \cdot 2} = {(- 6)}^{2}$

Rewrite the expression.

$49 h^{1} = {(- 6)}^{2}$

Simplify.

$49 h = {(- 6)}^{2}$

Simplify the right side.

Raise $- 6$ to the power of $2$ .

$49 h = 36$

Step 4

Divide each term in $49 h = 36$ by $49$ and simplify.

Divide each term in $49 h = 36$ by $49$ .

$\frac{49 h}{49} = \frac{36}{49}$

Simplify the left side.

Cancel the common factor of $49$ .

Cancel the common factor.

$\frac{49 h}{49} = \frac{36}{49}$

Divide $h$ by $1$ .

$h = \frac{36}{49}$

Step 5

Exclude the solutions that do not make $18 + 7 h^{\frac{1}{2}} = 12$ true.

$No solution$

Solve for h 18+7h^(1/2)=12

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