How do you solve $x - 6 = -x^2$ ?

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Answer 1 · 2018-03-05T14:53:38

See a solution process below:

First, put the equation in standard quadratic form:

$x - 6 = -x^2$

$color(red)(x^2) + x - 6 = color(red)(x^2) - x^2$

$x^2 + x - 6 = 0$

Next factor the quadratic as:

$(x + 3)(x - 2) = 0$

Now, solve each term on the left for $0$ :

Solution 1:

$x + 3 = 0$

$x + 3 - color(red)(3) = 0 - color(red)(3)$

$x + 0 = -3$

$x = -3$

Solution 2:

$x - 2 = 0$

$x - 2 + color(red)(2) = 0 + color(red)(2)$

$x - 0 = 2$

$x = 2$

The Solution Is:

$x = {-3, 2}$

How do you solve x - 6 = -x^2 x - 6 = -x^2 ?