How do you find the roots of #x^2-x=20#?

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Answer 1 · 2017-04-02T16:01:24

See below.

We can factor or graph the equation.

Factoring:
#x^2-x-20=0# becomes #(x-5)(x+4)=0#
So #x=5, -4#.

Graphing:
graph{x^2-x-20 [-4.335, 5.665, -2.06, 2.94]}
We see that the graph intersects the #x#-axis at #x=5,-4#, so those are our roots.

Answer 2 · 2017-04-02T16:03:03

See the entire solution process below:

First, subtract #color(red)(20)# from each side of the equation to put this equation into quadratic form:

#x^2 - x - color(red)(20) = 20 - color(red)(20)#

#x^2 - x - 20 = 0#

Because #4 - 5 = -1# and #4 xx -5 = -20# we can factor the left side of the equation as

#(x + 4)(x - 5) = 0#

Now, we solve each term on the right side of the equation to find the roots for this problem:

Solution 1)

#x + 4 = 0#

#x + 4 - color(red)(4) = 0 - color(red)(4)#

#x + 0 = -4#

#x = -4#

Solution 2)

#x - 5 = 0#

#x - 5 + color(red)(5) = 0 + color(red)(5)#

#x - 0 = 5#

#x = 5#

The roots are: #x = -4# and #x = 5#