What are the solutions of x^2-3x=-10?

Oct 22, 2015

The solutions are $\frac{3}{2} \pm i \cdot \frac{\sqrt{31}}{2}$, where $i = \sqrt{- 1}$ is the imaginary unit.

Explanation:

Write the equation in the form $a {x}^{2} + b x + c = 0$: ${x}^{2} - 3 x = - 10 \implies {x}^{2} - 3 x + 10 = 0$.

The solutions, by the quadratic formula, are then:

$x = \frac{- b \pm \sqrt{{b}^{2} - 4 a c}}{2 a} = \frac{3 \pm \sqrt{9 - 4 \cdot 1 \cdot 10}}{2 \cdot 1}$

$= \frac{3 \pm \sqrt{- 31}}{2} = \frac{3}{2} \pm i \cdot \frac{\sqrt{31}}{2}$, where $i = \sqrt{- 1}$ is the imaginary unit.

Oct 22, 2015

Imaginary numbers

Explanation:

=${x}^{2} - 3 x + 10 = 0$
graph{x^2-3x+10 [-23.11, 34.1, -3.08, 25.54]}
Using --- (b+ or - $\sqrt{{b}^{2} - 4 a c}$ )/ 2a

You'll see that it has complex roots, so by plotting a graph you can figure out the answer, but in the form

=
1.5 + 2.78388i
1.5 - 2.78388i