Question

Place the steps in the correct order to solve the following equation using the quadratic formula.

x^2 − 10x = 12

Answer 1

To solve the equation \( x^2 - 10x = 12 \) using the quadratic formula, you need to put the equation in standard form, \( ax^2 + bx + c = 0 \), identify the coefficients \( a \), \( b \), and \( c \), and then apply the quadratic formula.

Here are the steps in the correct order:

1. **Rearrange the equation into standard form:** Convert the equation \( x^2 - 10x = 12 \) to \( x^2 - 10x - 12 = 0 \) by subtracting 12 from both sides.

2. **Identify the coefficients:** From the equation \( x^2 - 10x - 12 = 0 \), identify:
- \( a = 1 \)
- \( b = -10 \)
- \( c = -12 \)

3. **Apply the quadratic formula:** The quadratic formula is given by
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
Substitute the values of \( a \), \( b \), and \( c \) into the formula.

4. **Calculate the discriminant:** Compute \( b^2 - 4ac \) to determine the number of real solutions.

5. **Compute the two possible solutions for \( x \):** Use the values from the quadratic formula to find both potential solutions by calculating \( \frac{-b + \sqrt{b^2 - 4ac}}{2a} \) and \( \frac{-b - \sqrt{b^2 - 4ac}}{2a} \).

By following these steps, you can successfully solve the quadratic equation.