- 4x - 19 = x ^ 2

Answer 1

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