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

See below.

The equation can be graphed or factored.

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See the entire solution process below:

In order to determine the roots of this issue, we now solve each term on the right side of the equation:

First Solution

Option 2)

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

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

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