Question

Solve the following quadratic by
completing the square.
f(x) = x2 + 10x - 1

Answer 1

x = -5 plus/minus sqrt( 26 )

Explanation:

Let's remember the binomial square formula

A^2 + 2AB + B^2 = (A + B)^2

We have:

x^2 + 2*5x -1

Hence, if we replace

A = x

B = 5

we get a perfect square: x^2 + 2*5x + 25 = (x + 5)^2. [++]

Based on this reasoning, let's set f(x) = 0

x^2 +10x -1 = 0

Let's add 26 on both terms:

x^2 +10x +25 = 26

Based on [++]: (x + 5)^2 = 26

Square root on both sides

(x + 5) = plus/minus sqrt (26)

x = -5 plus/minus sqrt (26)