Question
Write the quadratic equation in standard form:
2x - 1 = -x^2
2x - 1 = -x^2
Answers
Answered by
GPT-4o mini
To write the quadratic equation in standard form, we need to rearrange the equation \(2x - 1 = -x^2\) so that all terms are on one side and set equal to zero.
Starting with the given equation:
\[
2x - 1 = -x^2
\]
First, we can add \(x^2\) to both sides to move the \(x^2\) term to the left side of the equation:
\[
x^2 + 2x - 1 = 0
\]
Now, the equation is in standard form, which is:
\[
ax^2 + bx + c = 0
\]
where \(a = 1\), \(b = 2\), and \(c = -1\).
Thus, the quadratic equation in standard form is:
\[
x^2 + 2x - 1 = 0
\]
Starting with the given equation:
\[
2x - 1 = -x^2
\]
First, we can add \(x^2\) to both sides to move the \(x^2\) term to the left side of the equation:
\[
x^2 + 2x - 1 = 0
\]
Now, the equation is in standard form, which is:
\[
ax^2 + bx + c = 0
\]
where \(a = 1\), \(b = 2\), and \(c = -1\).
Thus, the quadratic equation in standard form is:
\[
x^2 + 2x - 1 = 0
\]
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