Question

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

Answer 1

Answer:

10.

Step-by-step 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.

Answer 2

Answer:  x = 10 is the positive root

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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.

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

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