Solve the Quadratic Equation: x²/2 + x - 4 = 0 Step-by-Step

To solve the equation $\frac{x^2}{2} + x - 4 = 0$, we'll use the quadratic formula. First, we need to rewrite the equation in standard quadratic form, $ax^2 + bx + c = 0$.

Start by multiplying the entire equation by 2 to eliminate the fraction:

Now, identify the coefficients:

• $a = 1$
• $b = 2$
• $c = -8$

Next, plug these coefficients into the quadratic formula:

Substitute $a = 1$, $b = 2$, and $c = -8$ into the formula:

Simplify inside the square root first:

Substitute back:

The square root of 36 is 6, so:

Calculate the two possible solutions:

Therefore, the solutions for the equation $\frac{x^2}{2} + x - 4 = 0$ are $x_1 = 2$ and $x_2 = -4$.