X^2-14x-4=0, solve by completing the square

The answer is: x = 7 - √53 or x = 7 + √53

The general quadratic equation is: ax² + bx + c = 0.

But, by completing the square we turn it into: a (x + d) ² + e = 0, where:

d = b/2a

e = c - b²/4a

Our quadratic equation is x² - 14x - 4 = 0, which is after rearrangement:

So, a = 1, b = - 14, c = - 4

Let's first calculate d and e:

d = b/2a = - 14/2*1 = - 14/2 = - 7

e = c - b²/4a = - 4 - (-14) ²/4*1 = - 4 - 196/4 = - 4 - 49 = - 53

By completing the square we have:

a (x + d) ² + e = 0

1 (x + (-7)) ² + (-53) = 0

(x - 7) ² - 53 = 0

(x - 7) ² = 53

x - 7 = + / - √53

x = 7 + / - √53

Therefore, the solutions are:

x = 7 - √53

or

x = 7 + √53