Question

What is the positive root of the equation x2 + 5x = 150?
ao

Answer 1

Answer: x = 10 is the positive root

================================================

Work Shown:

First get everything to one side

`x^2 + 5x = 150\\\\x^2 + 5x - 150 = 0\\\\`

Now use the quadratic formula

Plug in a = 1, b = 5, c = -150.

`x = (-b\pm√(b^2-4ac))/(2a)\\\\x = (-(5)\pm√((5)^2-4(1)(-150)))/(2(1))\\\\x = (-5\pm√(625))/(2)\\\\x = (-5\pm25)/(2)\\\\x = (-5+25)/(2) \ \text{ or } \ x = (-5-25)/(2)\\\\x = (20)/(2) \ \text{ or } \ x = (-30)/(2)\\\\x = 10 \ \text{ or } \ x = -15\\\\`

Factoring, completing the square, or graphing are alternative methods to get these two answers. We see that the positive root is x = 10.

Answer 2

10.

Explanation:

x^2 + 5x = 150

x^2 + 5x - 150 = 0

This equation will factor:

(x - 10)(x + 15) = 0

x - 10 = 0 or x + 15 = 0, so:

x = 10 or -15.