Question

Write the quadratic equation in standard form:
minus, 3, x, squared, plus, 2, x, minus, 10, equals, minus, 3, x
−3x
2
+2x−10=
−3x

Answer 1

To write the given equation in standard form, we need to set it equal to zero.

Starting with the equation:

\[
-3x^2 + 2x - 10 = -3x
\]

First, we'll move \(-3x\) to the left side by adding \(3x\) to both sides:

\[
-3x^2 + 2x + 3x - 10 = 0
\]

Now, combine the like terms:

\[
-3x^2 + 5x - 10 = 0
\]

The standard form of a quadratic equation is usually expressed as:

\[
ax^2 + bx + c = 0
\]

To write the equation in standard form, we can also multiply by \(-1\) to keep the leading coefficient positive (if needed):

\[
3x^2 - 5x + 10 = 0
\]

So, the standardized form of the quadratic equation is:

\[
3x^2 - 5x + 10 = 0
\]