what are all the sloutions to

y= 2x^2+25x+50

1 answer

To find the solutions to the quadratic equation y = 2x^2 + 25x + 50, we can set y equal to 0 and solve for x. This will give us the x-intercepts of the quadratic equation.

2x^2 + 25x + 50 = 0

To solve this equation, we can use the quadratic formula:

x = [-b ± √(b^2 - 4ac)] / 2a

Where a = 2, b = 25, and c = 50.

Plugging in these values, we get:

x = [-25 ± √(25^2 - 4*2*50)] / 2*2
x = [-25 ± √(625 - 400)] / 4
x = [-25 ± √225] / 4
x = [-25 ± 15] / 4

This gives us two solutions:
x = (-25 + 15) / 4 = -10 / 4 = -2.5
x = (-25 - 15) / 4 = -40 / 4 = -10

So the solutions to the quadratic equation y = 2x^2 + 25x + 50 are x = -2.5 and x = -10.