# How do you solve sqrt (3x + 4) + x = 8?

Mar 23, 2018

$\textcolor{b l u e}{x = 16}$

$\textcolor{b l u e}{x = 4}$

#### Explanation:

$\sqrt{3 x + 4} + x = 8$

Subtract $x$ from both sides:

$\sqrt{3 x + 4} = 8 - x$

Square both sides:

$3 x + 4 = {\left(8 - x\right)}^{2}$

Expand the bracket:

$3 x + 4 = 64 - 16 x + {x}^{2}$

Collect like terms:

${x}^{2} - 19 x + 60 = 0$

Factor:

${x}^{2} - 15 x - 4 x + 60$

$x \left(x - 15\right) - 4 \left(x - 15\right)$

$\left(x - 15\right) \left\{x - 4\right\}$

$\left(x - 16\right) \left(x - 4\right) = 0$

$x - 16 = 0 \implies \textcolor{b l u e}{x = 16}$

$x - 4 = 0 \implies \textcolor{b l u e}{x = 4}$

Mar 23, 2018

Solution: $x = 4 , x = 15$

#### Explanation:

$\sqrt{3 x + 4} + x = 8 \mathmr{and} \sqrt{3 x + 4} = 8 - x$ Squaring both sides

we get, $3 x + 4 = {\left(8 - x\right)}^{2} \mathmr{and} 3 x + 4 = {x}^{2} - 16 x + 64$ or

${x}^{2} - 16 x + 64 - 3 x - 4 = 0 \mathmr{and} {x}^{2} - 19 x + 60 = 0$ or

${x}^{2} - 15 x - 4 x + 60 = 0$ or

$x \left(x - 15\right) - 4 \left(x - 15\right) = 0 \mathmr{and} \left(x - 15\right) \left(x - 4\right) = 0 \therefore$

Either $x - 15 = 0 \therefore x = 15$ , or $x - 4 = 0 \therefore x = 4$

Check : $\sqrt{3 \cdot 4 + 4} + 4 = 8 \mathmr{and} \sqrt{16} + 4 = 8 \mathmr{and} 8 = 8$

$\sqrt{3 \cdot 15 + 4} + 15 = 8 \mathmr{and} \sqrt{49} + 15 = 8 \mathmr{and} - 7 + 15 = 8$

Solution: $x = 4 , x = 15$ [Ans]