# How do you solve sqrt(2x+10)-2sqrtx=0?

Jul 17, 2016

$x = 5$

#### Explanation:

Add $2 \sqrt{x}$ to both sides:

$\sqrt{2 x + 10} = 2 \sqrt{x}$

Square both sides:

$2 x + 10 = 4 x$

Subtract $2 x$ from both sides:

$10 = 2 x$

$\implies x = 5$

Jul 17, 2016

$\textcolor{b l u e}{5 = x}$

#### Explanation:

First get $- 2 \sqrt{x}$ to the other side.

$\sqrt{2 x + 10} \cancel{- 2 \sqrt{x} + 2 \sqrt{x}} = 0 + 2 \sqrt{x}$ - use additive inverse

$\sqrt{2 x + 10} = 2 \sqrt{x}$

Now square both sides. Remember that squaring a square root is equal to that number under the square root.

${\left(\sqrt{2 x + 10}\right)}^{2} = {\left(2 \sqrt{x}\right)}^{2}$ - square each side, because what you do to one side, you must do to the other

$2 x + 10 = {2}^{2} \cdot {\left(\sqrt{x}\right)}^{2}$ - Follow this concept: [${\left(a b\right)}^{x} = {a}^{x} \cdot {b}^{x}$]

$2 x + 10 = 4 x$

Now we can isolate the variable and identify $x$. Get $2 x$ to the other side and combine it with $4 x$, then divide out the coefficient to find $x$.

$\cancel{2 x - 2 x} + 10 = 4 x - 2 x$ - use additive inverse

$10 = 2 x$ - combine like terms

$\frac{10}{2} = \frac{\cancel{2} x}{\cancel{2}}$ - divide by two

$\textcolor{b l u e}{5 = x}$