x^2-5x-14=17

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Solution for x^2-5x-14=17 equation: 


Simplifying
x2 + -5x + -14 = 17

Reorder the terms:
-14 + -5x + x2 = 17

Solving
-14 + -5x + x2 = 17

Solving for variable 'x'.

Reorder the terms:
-14 + -17 + -5x + x2 = 17 + -17

Combine like terms: -14 + -17 = -31
-31 + -5x + x2 = 17 + -17

Combine like terms: 17 + -17 = 0
-31 + -5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '31' to each side of the equation.
-31 + -5x + 31 + x2 = 0 + 31

Reorder the terms:
-31 + 31 + -5x + x2 = 0 + 31

Combine like terms: -31 + 31 = 0
0 + -5x + x2 = 0 + 31
-5x + x2 = 0 + 31

Combine like terms: 0 + 31 = 31
-5x + x2 = 31

The x term is -5x.  Take half its coefficient (-2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
-5x + 6.25 + x2 = 31 + 6.25

Reorder the terms:
6.25 + -5x + x2 = 31 + 6.25

Combine like terms: 31 + 6.25 = 37.25
6.25 + -5x + x2 = 37.25

Factor a perfect square on the left side:
(x + -2.5)(x + -2.5) = 37.25

Calculate the square root of the right side: 6.103277808

Break this problem into two subproblems by setting 
(x + -2.5) equal to 6.103277808 and -6.103277808.


Subproblem 1
x + -2.5 = 6.103277808

Simplifying
x + -2.5 = 6.103277808

Reorder the terms:
-2.5 + x = 6.103277808

Solving
-2.5 + x = 6.103277808

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = 6.103277808 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = 6.103277808 + 2.5
x = 6.103277808 + 2.5

Combine like terms: 6.103277808 + 2.5 = 8.603277808
x = 8.603277808

Simplifying
x = 8.603277808


Subproblem 2
x + -2.5 = -6.103277808

Simplifying
x + -2.5 = -6.103277808

Reorder the terms:
-2.5 + x = -6.103277808

Solving
-2.5 + x = -6.103277808

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '2.5' to each side of the equation.
-2.5 + 2.5 + x = -6.103277808 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + x = -6.103277808 + 2.5
x = -6.103277808 + 2.5

Combine like terms: -6.103277808 + 2.5 = -3.603277808
x = -3.603277808

Simplifying
x = -3.603277808


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {8.603277808, -3.603277808}

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