Use the discriminant to determine how many and what kind of solutions the quadratic equation x^2-x=-(1)/(4) one real solution two complex (nonreal) solutions no real or complex solutions two real solutions

## Step 1: Convert the equation to standard form### Rewrite the given equation in standard quadratic form . Add to both sides to get .## Step 2: Identify coefficients### Identify the coefficients from the standard form: , , and .## Step 3: Calculate the discriminant### Use the formula for the discriminant, . Substitute the values: \( \Delta = (-1)^2 - 4(1)\left(\frac{1}{4}\right) \).## Step 4: Simplify the discriminant### Calculate .## Step 5: Determine the nature of the solutions### Since the discriminant is zero ( ), the quadratic equation has one real solution.