Question

Write the quadratic equation in standard form:
-6x^2 - 5x - 5 = -4x^2

Answer 1

To write the given equation in standard form, we start with the equation:

\[
-6x^2 - 5x - 5 = -4x^2
\]

First, we need to move all terms to one side of the equation. We can do this by adding \(4x^2\) to both sides:

\[
-6x^2 + 4x^2 - 5x - 5 = 0
\]

Combine the \(x^2\) terms:

\[
(-6x^2 + 4x^2) - 5x - 5 = 0
\]
\[
-2x^2 - 5x - 5 = 0
\]

Next, we want to express it in standard form \(ax^2 + bx + c = 0\). Since we want the leading coefficient \(a\) to be positive, we can multiply the entire equation by -1:

\[
2x^2 + 5x + 5 = 0
\]

Thus, the quadratic equation in standard form is:

\[
2x^2 + 5x + 5 = 0
\]