Question

Solve: x^2 - 14x + 58 = 0

Answer 1

We can use the quadratic formula to solve this equation:

$x=\frac{-b}{2a}+/-\frac{\sqrt[]{b^2-4ac}}{2a}$

Then, we have:

a = 1

b = -14

c = 58

Thus

$x=\frac{-(-14)}{2\cdot1}+\frac{\sqrt[]{(-14)^2-4(1)(58)}}{2\cdot1}\Rightarrow x=\frac{14}{2}+\frac{\sqrt[]{196-232}}{2}$

As we can see, the result will be a complex number solution:

$x=7+\frac{\sqrt[]{-36}}{2}\Rightarrow x=7+\frac{\sqrt[]{36i^2}}{2}\Rightarrow x=7+\frac{\sqrt[]{36}}{2}i\Rightarrow x=7+\frac{6}{2}i\Rightarrow x=7+3i$

We have to remember that:

$i^2=-1$

Then, one of the solution is x = 7 + 3i. Therefore, according to the quadratic formula, the other solution is x = 7 - 3i.

The solutions are x = 7 + 3i and x = 7 - 3i.