Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Feb 14, 2024

Find the equation equivalent to $2x + 180 = 2x^2$ . Options: $2x^2 + 2x + 180 = 0$ , $2x^2 - 2x + 180 = 0$ , $2x^2 + 2x - 180 = 0$ , $2x^2 - 2x - 180 = 0$ .

STEP 1

Assumptions
1. We are given the equation $2x + 180 = 2x^2$ .
2. We are looking for an equivalent equation in the form $2x^2 + ax + b = 0$ , where $a$ and $b$ are constants to be determined.

STEP 2

To find an equivalent equation, we need to bring all terms to one side of the equation to set it equal to zero. This is the standard form of a quadratic equation.
$2x^2 - (2x + 180) = 0$

STEP 3

Distribute the negative sign across the terms in the parentheses.
$2x^2 - 2x - 180 = 0$

STEP 4

Now we compare the equation obtained in STEP_3 with the answer choices to find the equivalent equation.
The equivalent equation to the given equation $2x + 180 = 2x^2$ is:
$2x^2 - 2x - 180 = 0$

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