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

Question

Julia Adams · Accepted Answer

See below.

The equation can be graphed or factored. 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.

Kennedy Adams · Answer

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# In order to determine the roots of this issue, we now solve each term on the right side of the equation: First Solution #x + 4 = 0# #x + 4 - color(red)(4) = 0 - color(red)(4)# #x + 0 = -4# #x = -4# Option 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#

Genesis Allen · Answer

undefined To find the roots of the equation $x^2 - x = 20$, follow these steps:

1. Rewrite the equation in standard quadratic form: $x^2 - x - 20 = 0$.
2. Use the quadratic formula: $x = \frac{{-b \pm \sqrt{{b^2 - 4ac}}}}{{2a}}$, where $a = 1$, $b = -1$, and $c = -20$.
3. Plug in the values: $x = \frac{{-(-1) \pm \sqrt{{(-1)^2 - 4(1)(-20)}}}}{{2(1)}}$.
4. Simplify the expression under the square root: $x = \frac{{1 \pm \sqrt{{1 + 80}}}}{2}$.
5. Simplify further: $x = \frac{{1 \pm \sqrt{{81}}}}{2}$.
6. Find the square root of 81: $x = \frac{{1 \pm 9}}{2}$.
7. Find both roots: $x_1 = \frac{{1 + 9}}{2} = 5$ and $x_2 = \frac{{1 - 9}}{2} = -4$.

Therefore, the roots of the equation $x^2 - x = 20$ are $x = 5$ and $x = -4$.