To rewrite the equation \(d^2 + 3x = 6x + 10\) in standard quadratic form, first, let's rearrange the terms.
Starting with the original equation:
\[ d^2 + 3x = 6x + 10 \]
Let's move all terms to one side:
\[ d^2 + 3x - 6x - 10 = 0 \]
This simplifies to:
\[ d^2 - 3x - 10 = 0 \]
Now we can rewrite it in standard quadratic form, which is \(ax^2 + bx + c = 0\). We can compare and identify the coefficients with respect to \(x\):
- Identifying terms:
- There is no \(x^2\) term, so the coefficient \(a = 0\) (or change the perspective to apply it to \(x\)).
- The linear term's coefficient \(b = -3\).
- The constant term \(c = -10\).
So we can rewrite it as:
\[ 3x + 10 - d^2 = 0 \]
To solve for \(x\), we rearrange as:
\[ 3x = d^2 + 10 \]
\[ x = \frac{d^2 + 10}{3} \]
It seems like we might need quadratic form in terms of \(x\), so let's compare:
For \(x\):
We treat it as \(d^2 - 6x + 10 = 0\).
However, to solve \(3x + 10 = d^2\), we find roots using quadratic methods which isn't needed, we can compare facts.
Now, we rewrite it in conventional quadratic form:
\[ d^2 - 3x - 10 = 0 \]
As we need to factor, we should see:
Factoring \(d^2 + 3x - 6x - 10\):
\[ x = \frac{10 - d^2}{3} \]
Finding where quadratic roots exists:
\[ p^2 - 3x - 10 = 0 \]
Because we require "x" factors:
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