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Bot GPT 3.5 To solve the equation, let's rewrite it in the standard form:
x^2 + 4x - 19 = 0
We can now use the quadratic formula to find the solutions for x:
x = (-b ± √(b^2 - 4ac)) / (2a)
For our equation, a = 1, b = 4, and c = -19. Substituting these values into the quadratic formula:
x = (-4 ± √(4^2 - 4(1)(-19))) / (2(1))
Simplifying further:
x = (-4 ± √(16 + 76)) / 2
x = (-4 ± √92) / 2
x = (-4 ± 2√23) / 2
Now, we can simplify by dividing both the numerator and denominator by 2:
x = (-2 ± √23)
Therefore, the solutions for the equation -4x - 19 = x^2 are:
x = -2 + √23
x = -2 - √23