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Place the steps in the correct order to solve the following equation using the quadratic formula. x^2 − 10x = 12Asked by T-Swizzle
Place the steps in the correct order to solve the following equation using the quadratic formula: x^2 - 10x = 12
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Answered by
GPT-4o mini
To solve the equation \(x^2 - 10x = 12\) using the quadratic formula, we first need to rearrange the equation into standard form \(ax^2 + bx + c = 0\). Here are the steps in the correct order:
1. **Rearrange the equation**: Move all terms to one side to set the equation to zero:
\[
x^2 - 10x - 12 = 0
\]
2. **Identify coefficients**: Identify the coefficients \(a\), \(b\), and \(c\) from the equation \(ax^2 + bx + c = 0\):
- \(a = 1\)
- \(b = -10\)
- \(c = -12\)
3. **Use the quadratic formula**: Recall the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
4. **Calculate the discriminant**: Compute the value of \(b^2 - 4ac\):
\[
b^2 - 4ac = (-10)^2 - 4(1)(-12) = 100 + 48 = 148
\]
5. **Substitute into the formula**: Plug the values of \(a\), \(b\), and the discriminant into the quadratic formula:
\[
x = \frac{-(-10) \pm \sqrt{148}}{2(1)} = \frac{10 \pm \sqrt{148}}{2}
\]
6. **Simplify the square root**: Simplify \(\sqrt{148}\):
\[
\sqrt{148} = \sqrt{4 \cdot 37} = 2\sqrt{37}
\]
7. **Substitute back and simplify**:
\[
x = \frac{10 \pm 2\sqrt{37}}{2} = 5 \pm \sqrt{37}
\]
8. **Write the final solutions**: The final solutions are:
\[
x = 5 + \sqrt{37} \quad \text{and} \quad x = 5 - \sqrt{37}
\]
By following these steps in order, you can effectively solve the quadratic equation using the quadratic formula.
1. **Rearrange the equation**: Move all terms to one side to set the equation to zero:
\[
x^2 - 10x - 12 = 0
\]
2. **Identify coefficients**: Identify the coefficients \(a\), \(b\), and \(c\) from the equation \(ax^2 + bx + c = 0\):
- \(a = 1\)
- \(b = -10\)
- \(c = -12\)
3. **Use the quadratic formula**: Recall the quadratic formula:
\[
x = \frac{-b \pm \sqrt{b^2 - 4ac}}{2a}
\]
4. **Calculate the discriminant**: Compute the value of \(b^2 - 4ac\):
\[
b^2 - 4ac = (-10)^2 - 4(1)(-12) = 100 + 48 = 148
\]
5. **Substitute into the formula**: Plug the values of \(a\), \(b\), and the discriminant into the quadratic formula:
\[
x = \frac{-(-10) \pm \sqrt{148}}{2(1)} = \frac{10 \pm \sqrt{148}}{2}
\]
6. **Simplify the square root**: Simplify \(\sqrt{148}\):
\[
\sqrt{148} = \sqrt{4 \cdot 37} = 2\sqrt{37}
\]
7. **Substitute back and simplify**:
\[
x = \frac{10 \pm 2\sqrt{37}}{2} = 5 \pm \sqrt{37}
\]
8. **Write the final solutions**: The final solutions are:
\[
x = 5 + \sqrt{37} \quad \text{and} \quad x = 5 - \sqrt{37}
\]
By following these steps in order, you can effectively solve the quadratic equation using the quadratic formula.
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