Questions: Solve for x if 2(5x+2)^2=48 x=(-2+2 sqrt(24))/5 and x=(-2-2 sqrt(24))/5 x=(-2+2 sqrt(24))/2 and x=(-2-2 sqrt(24))/2 x=(-2+2 sqrt(6))/5 and x=(-2-2 sqrt(6))/5 x=(-2+2 sqrt(6))/2 and x=(-2-2 sqrt(6))/2

Transcript text: Solve for x if $2(5 x+2)^{2}=48$ $x=\frac{-2+2 \sqrt{24}}{5}$ and $x=\frac{-2-2 \sqrt{24}}{5}$ $x=\frac{-2+2 \sqrt{24}}{2}$ and $x=\frac{-2-2 \sqrt{24}}{2}$ $x=\frac{-2+2 \sqrt{6}}{5}$ and $x=\frac{-2-2 \sqrt{6}}{5}$ $x=\frac{-2+2 \sqrt{6}}{2}$ and $x=\frac{-2-2 \sqrt{6}}{2}$

Solution

Solution Steps

To solve the equation $2(5x + 2)^2 = 48$, we need to follow these steps:

Divide both sides of the equation by 2 to simplify it.
Take the square root of both sides to solve for $5x + 2$.
Isolate $x$ by solving the resulting linear equations.

Step 1: Simplify the Equation

Starting with the equation $2(5x + 2)^2 = 48$, we divide both sides by 2 to simplify: \[ (5x + 2)^2 = 24 \]

Step 2: Take the Square Root

Next, we take the square root of both sides: \[ 5x + 2 = \pm \sqrt{24} \] Since $\sqrt{24} = 2\sqrt{6}$, we can rewrite the equation as: \[ 5x + 2 = \pm 2\sqrt{6} \]

Step 3: Isolate $x$

Now, we isolate $x$ by solving the two cases:

$5x + 2 = 2\sqrt{6}$
$5x + 2 = -2\sqrt{6}$

For the first case: \[ 5x = 2\sqrt{6} - 2 \implies x = \frac{2\sqrt{6} - 2}{5} \]

For the second case: \[ 5x = -2\sqrt{6} - 2 \implies x = \frac{-2\sqrt{6} - 2}{5} \]

Final Answer

The solutions for $x$ are: \[ x = \frac{2\sqrt{6} - 2}{5} \quad \text{and} \quad x = \frac{-2\sqrt{6} - 2}{5} \] Thus, the final boxed answers are: \[ \boxed{x = \frac{2\sqrt{6} - 2}{5}} \quad \text{and} \quad \boxed{x = \frac{-2\sqrt{6} - 2}{5}} \]

Was this solution helpful?

Unhelpful

Helpful

Questions asked by other users

< Previous Next >

Thank you for your feedback.

Copied!