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 = -14/21 = -14/2 = -7
e = c - b²/4a = -4 - (-14)²/41 = -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
