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, we first need to rearrange the equation into the standard form \( ax^2 + bx + c = 0 \). Here are the steps in the correct order:

1. **Rearrange the equation to standard form**: Move 12 to the left side of the equation:
\[
x^2 - 10x - 12 = 0
\]

2. **Identify the coefficients**: From the standard form \( ax^2 + bx + c = 0 \), we identify:
- \( a = 1 \) (coefficient of \( x^2 \))
- \( b = -10 \) (coefficient of \( x \))
- \( c = -12 \) (constant term)

3. **Apply the quadratic formula**: The quadratic formula is given by:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]

4. **Calculate the discriminant**: Compute \( b^2 - 4ac \):
\[
b^2 - 4ac = (-10)^2 - 4(1)(-12) = 100 + 48 = 148
\]

5. **Substitute into the quadratic formula**: Plug the values into the formula:
\[
x = \frac{-(-10) \pm \sqrt{148}}{2(1)} = \frac{10 \pm \sqrt{148}}{2}
\]

6. **Simplify the expression**: Simplify \( \sqrt{148} \):
\[
\sqrt{148} = 2\sqrt{37}
\]
Therefore:
\[
x = \frac{10 \pm 2\sqrt{37}}{2} = 5 \pm \sqrt{37}
\]

7. **Write the final answers**:
\[
x = 5 + \sqrt{37} \quad \text{and} \quad x = 5 - \sqrt{37}
\]

So the steps to solve the equation using the quadratic formula are as follows:
1. Rearrange the equation.
2. Identify the coefficients.
3. Apply the quadratic formula.
4. Calculate the discriminant.
5. Substitute into the quadratic formula.
6. Simplify the expression.
7. Write the final answers.