Solve the Quadratic Equation: Find x in 4x² + 2x + 8 = x + 12 + x

To solve this problem, we'll follow these steps:

• Step 1: Simplify both sides of the equation.
• Step 2: Rearrange terms to form a quadratic equation.
• Step 3: Solve the quadratic equation using an appropriate method, such as factoring or applying the quadratic formula.

Now, let's work through each step:

Step 1: Simplify both sides of the equation:

$4x^2 + 8 + 2x = x + 12 + x$

The right-hand side can be simplified:

$x + x + 12 = 2x + 12$

This yields the equation:

$4x^2 + 8 + 2x = 2x + 12$

Step 2: Rearrange the terms to form a quadratic equation. Subtract $2x + 12$ from both sides:

$4x^2 + 8 + 2x - 2x - 12 = 0$

Combining like terms gives:

$4x^2 - 4 = 0$

Step 3: Solve the resulting quadratic equation:

First, we add 4 to both sides:

$4x^2 = 4$

Next, divide both sides by 4:

$x^2 = 1$

Now, apply the square root to both sides:

$x = \pm 1$

Therefore, the solutions to the quadratic equation are

$x = \pm 1$.

The correct answer is choice 2: ±1.