Question

x^2+20x=−75 quadratic formula

Answer 1

To solve the equation x^2 + 20x = -75 using the quadratic formula, we first need to rearrange the equation in the form ax^2 + bx + c = 0.

So, we have x^2 + 20x + 75 = 0.

Now, we can identify the coefficients:
a = 1, b = 20, and c = 75.

Next, we can plug these values into the quadratic formula:
x = (-b ± √(b^2 - 4ac)) / 2a

x = (-20 ± √(20^2 - 4*1*75)) / 2*1
x = (-20 ± √(400 - 300)) / 2
x = (-20 ± √100) / 2
x = (-20 ± 10) / 2

So, the solutions for x are:
x = (-20 + 10) / 2 = -10 / 2 = -5
x = (-20 - 10) / 2 = -30 / 2 = -15

Therefore, the solutions for the equation x^2 + 20x = -75 are x = -5 and x = -15.