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

Solve the following equation:

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

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:

The right-hand side can be simplified:

This yields the equation:

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

Combining like terms gives:

Step 3: Solve the resulting quadratic equation:

First, we add 4 to both sides:

Next, divide both sides by 4:

Now, apply the square root to both sides:

Therefore, the solutions to the quadratic equation are

$x = \pm 1$.

The correct answer is choice 2: ±1.