Math question, help needed?

Question

Solve each equation, if possible, Write irrational numbers in simplest radical form. Describe the strategy you used to get your solution and tell why you chose that Strategy.


1. x^2 - 5x -7 = 0

Answer 1

The quadratic can't be factored. We can use 2 methods:

Method 1: (Formula method)
x^2 - 5x - 7 = 0

Using quadratic formula,
x = [5 +/- sqrt (25 + 28)]/2
x = [5 +/- sqrt 53]/2

Method 2: (Completing the square)
x^2 - 5x - 7 = 0
{(x)^2 - 2(x)(5/2) + (5/2)^2} - (5/2)^2 - 7 = 0
(x - 5/2)^2 - 25/4 - 7 = 0
(x - 5/2)^2 - 28/4 - 25/4 = 0
(x - 5/2)^2 - 53/4 = 0
(x - 5/2)^2 = 53/4
x - 5/2 = +/- sqrt (53/4)
x - 5/2 = +/- (sqrt 53)/2
x = (5/2) +/- [sqrt (53)]/2
x = [5 +/- (sqrt 53)]/2

Answer 2

My strategy will be to use the quadratic formula since you cannot factor that quadratic.

x = -b +/- sqrt (b^2 - 4ac) /2a
= 5 +/- sqrt ((-5)^2 - 4(1)(-7))/2
= 5+/- sqrt (25 + 28) /2
= 5+/- sqrt (53)/2

Therefore, the answer is

[5 - sqrt(53)] / 2

and

[5 + sqrt(53)] /2

Good luck.