Question

Use the quadratic formula to solve the equation. If necessary, round to the nearest hundredth.

x^2 - 20 = x

a. 5, 4
b. -5, -4
c. -5, 4
d. 5, -4

Answer 1

The correct answer option is d. 5, -4.

Explanation:

We are given the following equation and we are to solve it using the quadratic formula:

`x^2 - 20 = x`

Re-arranging this equation in order of decreasing power:

`x^2-x-20=0`

Using the quadratic formula:

`x = \frac {-b + - √(b^2 - 4ac) }{2a}`

Substituting the given values in the formula to get:

`x=(-(-1)+-√((-1)^2-4(1)(-20)) )/(2(1))`

`x=(1+-√(81) )/(2)`

`x=5, x=-4`

Answer 2

Option d is correct 5, -4

Explanation:

Given equation x² - 20 = x

rewriting the above equation

x² - x - 20 = 0

`x = \frac{-b +- \sqrt{b^(2)-4ac}}{2a}`

where a = 1; b = -1; c = -20

put values of a, b and c in the formula

`x = \frac{-(-1) +- \sqrt{(-1)^(2)-4(1)(-20)}}{2(1)}`

`x = (1 +- √(1+80))/(2)`

`x = (1 +- √(81))/(2)`

`x = (1 +- 9)/(2)`

`x = (1 + 9)/(2)`

x = 5

`x = (1 - 9)/(2)`

x = -4