Evaluate 1+ square root of 5x+5=5

$1 + \sqrt{5 x + 5} = 5$

Step 1

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

Subtract $1$ from both sides of the equation.

$\sqrt{5 x + 5} = 5 - 1$

Subtract $1$ from $5$ .

$\sqrt{5 x + 5} = 4$

Step 2

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

${\sqrt{5 x + 5}}^{2} = 4^{2}$

Step 3

Simplify each side of the equation.

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

${({(5 x + 5)}^{\frac{1}{2}})}^{2} = 4^{2}$

Simplify the left side.

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

Multiply the exponents in ${({(5 x + 5)}^{\frac{1}{2}})}^{2}$ .

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

${(5 x + 5)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Cancel the common factor of $2$ .

Cancel the common factor.

${(5 x + 5)}^{\frac{1}{2} \cdot 2} = 4^{2}$

Rewrite the expression.

${(5 x + 5)}^{1} = 4^{2}$

Simplify.

$5 x + 5 = 4^{2}$

Simplify the right side.

Raise $4$ to the power of $2$ .

$5 x + 5 = 16$

Step 4

Solve for $x$ .

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

Subtract $5$ from both sides of the equation.

$5 x = 16 - 5$

Subtract $5$ from $16$ .

$5 x = 11$

Divide each term in $5 x = 11$ by $5$ and simplify.

Divide each term in $5 x = 11$ by $5$ .

$\frac{5 x}{5} = \frac{11}{5}$

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

$\frac{5 x}{5} = \frac{11}{5}$

Divide $x$ by $1$ .

$x = \frac{11}{5}$

Step 5

The result can be shown in multiple forms.

Exact Form:

$x = \frac{11}{5}$

Decimal Form:

$x = 2.2$

Mixed Number Form:

$x = 2 \frac{1}{5}$

Evaluate 1+ square root of 5x+5=5

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