Final answer:
To solve the equation x^2 + 5x - 50 = 0, we can use the quadratic formula. The solutions for x are 5 and -10.
Step-by-step explanation:
To solve the equation x2 + 5x - 50 = 0, we can use the quadratic formula. The quadratic formula states that if we have an equation of the form ax2 + bx + c = 0, the solutions for x are given by:
x = (-b ± √(b2 - 4ac))/(2a)
In this case, a = 1, b = 5, and c = -50. Plugging in these values into the quadratic formula, we get:
x = (-5 ± √(52 - 4(1)(-50)))/(2(1))
Simplifying this further, we have:
x = (-5 ± √(25 + 200))/2
x = (-5 ± √225)/2
Since √225 = 15, we have:
x = (-5 ± 15)/2
So the solutions for x are x = (-5 + 15)/2 = 5 and x = (-5 - 15)/2 = -10.
To check our solutions, we can substitute them back into the original equation and see if both sides are equal. If we substitute x = 5, we get:
(52) + 5(5) - 50 = 25 + 25 - 50 = 0
If we substitute x = -10, we get:
((-10)2) + 5(-10) - 50 = 100 - 50 - 50 = 0
Both solutions satisfy the equation, so our solutions are correct.