Solve for x 27=7+5 square root of x

$27 = 7 + 5 \sqrt{x}$

Step 1

Rewrite the equation as $7 + 5 \sqrt{x} = 27$ .

$7 + 5 \sqrt{x} = 27$

Step 2

Move all terms not containing $5 \sqrt{x}$ to the right side of the equation.

Subtract $7$ from both sides of the equation.

$5 \sqrt{x} = 27 - 7$

Subtract $7$ from $27$ .

$5 \sqrt{x} = 20$

Step 3

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

${(5 \sqrt{x})}^{2} = 20^{2}$

Step 4

Simplify each side of the equation.

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

${(5 x^{\frac{1}{2}})}^{2} = 20^{2}$

Simplify the left side.

Simplify ${(5 x^{\frac{1}{2}})}^{2}$ .

Apply the product rule to $5 x^{\frac{1}{2}}$ .

$5^{2} {(x^{\frac{1}{2}})}^{2} = 20^{2}$

Raise $5$ to the power of $2$ .

$25 {(x^{\frac{1}{2}})}^{2} = 20^{2}$

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

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

$25 x^{\frac{1}{2} \cdot 2} = 20^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

$25 x^{\frac{1}{2} \cdot 2} = 20^{2}$

Rewrite the expression.

$25 x^{1} = 20^{2}$

Simplify.

$25 x = 20^{2}$

Simplify the right side.

Raise $20$ to the power of $2$ .

$25 x = 400$

Step 5

Divide each term in $25 x = 400$ by $25$ and simplify.

Divide each term in $25 x = 400$ by $25$ .

$\frac{25 x}{25} = \frac{400}{25}$

Simplify the left side.

Cancel the common factor of $25$ .

Cancel the common factor.

$\frac{25 x}{25} = \frac{400}{25}$

Divide $x$ by $1$ .

$x = \frac{400}{25}$

Simplify the right side.

Divide $400$ by $25$ .

$x = 16$

Solve for x 27=7+5 square root of x

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