Question

Which equation could be solved using this application of the quadratic formula?



A.
-2x2 − 8 = 10x − 3
B.
3x2 − 8x − 10 = 4
C.
3x2 + 8x − 10 = -8
D.
-2x2 + 8x − 3 = 4

Answer 1

To determine which equation can be solved using the quadratic formula, we need to identify a quadratic equation in standard form, which is \( ax^2 + bx + c = 0 \).

Let's analyze each option to see if we can rewrite the equations in this format:

**A.** \(-2x^2 - 8 = 10x - 3\)

Rearranging gives:
\[
-2x^2 - 10x - 8 + 3 = 0 \implies -2x^2 - 10x - 5 = 0
\]
This can be written as:
\[
2x^2 + 10x + 5 = 0
\]
This is a valid quadratic equation.

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**B.** \(3x^2 - 8x - 10 = 4\)

Rearranging yields:
\[
3x^2 - 8x - 10 - 4 = 0 \implies 3x^2 - 8x - 14 = 0
\]
This is also a valid quadratic equation.

---

**C.** \(3x^2 + 8x - 10 = -8\)

Rearranging gives:
\[
3x^2 + 8x - 10 + 8 = 0 \implies 3x^2 + 8x - 2 = 0
\]
This is another valid quadratic equation.

---

**D.** \(-2x^2 + 8x - 3 = 4\)

Rearranging yields:
\[
-2x^2 + 8x - 3 - 4 = 0 \implies -2x^2 + 8x - 7 = 0
\]
This can be rewritten as:
\[
2x^2 - 8x + 7 = 0
\]
This is also a valid quadratic equation.

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All four options represent quadratic equations after rearranging. Therefore, any of these equations, A, B, C, or D, can be solved using the quadratic formula.

If you need to choose one specific answer based on the context or any additional information, please specify. Otherwise, all options can indeed be solved with the quadratic formula.