Question
Write the quadratic equation in standard form:
minus, 6, x, squared, plus, 3, x, plus, 13, equals, minus, 2, x, squared
−6x
2
+3x+13=
−2x
2
minus, 6, x, squared, plus, 3, x, plus, 13, equals, minus, 2, x, squared
−6x
2
+3x+13=
−2x
2
Answers
Answered by
GPT-4o mini
To write the given equation in standard form, we first start with the equation:
\[
-6x^2 + 3x + 13 = -2x^2
\]
Next, we want to rearrange the equation so that all terms are on one side and the equation is set equal to zero. We can do this by adding \(2x^2\) to both sides:
\[
-6x^2 + 2x^2 + 3x + 13 = 0
\]
Now, combine the \(x^2\) terms:
\[
(-6x^2 + 2x^2) + 3x + 13 = 0
\]
This simplifies to:
\[
-4x^2 + 3x + 13 = 0
\]
To write the quadratic in standard form, we typically prefer the leading coefficient to be positive. Therefore, multiply the entire equation by -1:
\[
4x^2 - 3x - 13 = 0
\]
So the quadratic equation in standard form is:
\[
4x^2 - 3x - 13 = 0
\]
\[
-6x^2 + 3x + 13 = -2x^2
\]
Next, we want to rearrange the equation so that all terms are on one side and the equation is set equal to zero. We can do this by adding \(2x^2\) to both sides:
\[
-6x^2 + 2x^2 + 3x + 13 = 0
\]
Now, combine the \(x^2\) terms:
\[
(-6x^2 + 2x^2) + 3x + 13 = 0
\]
This simplifies to:
\[
-4x^2 + 3x + 13 = 0
\]
To write the quadratic in standard form, we typically prefer the leading coefficient to be positive. Therefore, multiply the entire equation by -1:
\[
4x^2 - 3x - 13 = 0
\]
So the quadratic equation in standard form is:
\[
4x^2 - 3x - 13 = 0
\]