Let $a$ and $b$ be the roots of $x^2 + 7x - 4 = -x^2 + 9x + 6$. Find $(a + 3) + (b + 3).$
x^2 + 7x - 4 = -x^2 + 9x + 6, combine like terms:
2x^2 - 2x - 10 = 0
x^2 - x - 5 = 0
By vieta's, the sum of the roots a + b = -1 * the second term / the leading coefficient = 1.
Thus, a + 3 + b + 3 = a + b + 6 = 7
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