Question
Write the quadratic equation in standard form:
-5 - 2x - x^2= 2x^2 + 3x
-5 - 2x - x^2= 2x^2 + 3x
Answers
Answered by
GPT-4o mini
To write the given equation in standard form, we first need to combine all the terms on one side of the equation and set it equal to zero. The original equation is:
\[
-5 - 2x - x^2 = 2x^2 + 3x
\]
First, let's move all the terms from the right side to the left side of the equation by subtracting \(2x^2\) and \(3x\) from both sides:
\[
-5 - 2x - x^2 - 2x^2 - 3x = 0
\]
Now, combine like terms:
\[
-5 - 5x - 3x^2 = 0
\]
Rearranging it gives:
\[
-3x^2 - 5x - 5 = 0
\]
To write this in standard form \(Ax^2 + Bx + C = 0\), we can multiply the entire equation by \(-1\) to make the leading coefficient positive:
\[
3x^2 + 5x + 5 = 0
\]
Thus, the quadratic equation in standard form is:
\[
3x^2 + 5x + 5 = 0
\]
\[
-5 - 2x - x^2 = 2x^2 + 3x
\]
First, let's move all the terms from the right side to the left side of the equation by subtracting \(2x^2\) and \(3x\) from both sides:
\[
-5 - 2x - x^2 - 2x^2 - 3x = 0
\]
Now, combine like terms:
\[
-5 - 5x - 3x^2 = 0
\]
Rearranging it gives:
\[
-3x^2 - 5x - 5 = 0
\]
To write this in standard form \(Ax^2 + Bx + C = 0\), we can multiply the entire equation by \(-1\) to make the leading coefficient positive:
\[
3x^2 + 5x + 5 = 0
\]
Thus, the quadratic equation in standard form is:
\[
3x^2 + 5x + 5 = 0
\]