To find the equivalent quadratic equation, we need to simplify the expression given in the question: x² + 12 + 11x² + 1 + 24 = 0.
Let’s first combine like terms. The x² terms are:
- x² + 11x² = 12x²
Now, let’s add the constant terms:
- 12 + 1 + 24 = 37
So, the equation now looks like this:
12x² + 37 = 0.
This is one way to write an equivalent quadratic equation. However, traditionally, a standard form of a quadratic equation is written in the format ax² + bx + c = 0, where a, b, and c are constants.
If we transform our simplified equation to align with the standard form, we could move 37 to the right-hand side, giving:
12x² = -37
This is the equivalent quadratic equation, albeit in a less common form. We could also say:
12x² + 0x + 37 = 0, where b = 0.
Thus, the equivalent quadratic equation can be expressed clearly as:
12x² + 0x + 37 = 0, or simply 12x² + 37 = 0.