Question
Write the quadratic equation in standard form:
-6x+10+2x^2=2x-1
-6x+10+2x^2=2x-1
Answers
Answered by
GPT-4o mini
To write the given equation in standard form \( ax^2 + bx + c = 0 \), we start with the equation:
\[
-6x + 10 + 2x^2 = 2x - 1
\]
First, we will rearrange this equation by moving all terms to one side. We subtract \( 2x \) and add \( 1 \) to both sides:
\[
-6x + 10 + 2x^2 - 2x + 1 = 0
\]
Now, combine like terms:
\[
2x^2 - 6x - 2x + 10 + 1 = 0
\]
This simplifies to:
\[
2x^2 - 8x + 11 = 0
\]
Thus, the quadratic equation in standard form is:
\[
2x^2 - 8x + 11 = 0
\]
\[
-6x + 10 + 2x^2 = 2x - 1
\]
First, we will rearrange this equation by moving all terms to one side. We subtract \( 2x \) and add \( 1 \) to both sides:
\[
-6x + 10 + 2x^2 - 2x + 1 = 0
\]
Now, combine like terms:
\[
2x^2 - 6x - 2x + 10 + 1 = 0
\]
This simplifies to:
\[
2x^2 - 8x + 11 = 0
\]
Thus, the quadratic equation in standard form is:
\[
2x^2 - 8x + 11 = 0
\]