0=x^2-14x-3

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Solution for 0=x^2-14x-3 equation:


Simplifying
0 = x2 + -14x + -3

Reorder the terms:
0 = -3 + -14x + x2

Solving
0 = -3 + -14x + x2

Solving for variable 'x'.

Combine like terms: 0 + 3 = 3
3 + 14x + -1x2 = -3 + -14x + x2 + 3 + 14x + -1x2

Reorder the terms:
3 + 14x + -1x2 = -3 + 3 + -14x + 14x + x2 + -1x2

Combine like terms: -3 + 3 = 0
3 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2
3 + 14x + -1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
3 + 14x + -1x2 = 0 + x2 + -1x2
3 + 14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
3 + 14x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-3 + -14x + x2 = 0

Move the constant term to the right:

Add '3' to each side of the equation.
-3 + -14x + 3 + x2 = 0 + 3

Reorder the terms:
-3 + 3 + -14x + x2 = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -14x + x2 = 0 + 3
-14x + x2 = 0 + 3

Combine like terms: 0 + 3 = 3
-14x + x2 = 3

The x term is -14x.  Take half its coefficient (-7).
Square it (49) and add it to both sides.

Add '49' to each side of the equation.
-14x + 49 + x2 = 3 + 49

Reorder the terms:
49 + -14x + x2 = 3 + 49

Combine like terms: 3 + 49 = 52
49 + -14x + x2 = 52

Factor a perfect square on the left side:
(x + -7)(x + -7) = 52

Calculate the square root of the right side: 7.211102551

Break this problem into two subproblems by setting 
(x + -7) equal to 7.211102551 and -7.211102551.

Subproblem 1

x + -7 = 7.211102551 Simplifying x + -7 = 7.211102551 Reorder the terms: -7 + x = 7.211102551 Solving -7 + x = 7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = 7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.211102551 + 7 x = 7.211102551 + 7 Combine like terms: 7.211102551 + 7 = 14.211102551 x = 14.211102551 Simplifying x = 14.211102551

Subproblem 2

x + -7 = -7.211102551 Simplifying x + -7 = -7.211102551 Reorder the terms: -7 + x = -7.211102551 Solving -7 + x = -7.211102551 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7' to each side of the equation. -7 + 7 + x = -7.211102551 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.211102551 + 7 x = -7.211102551 + 7 Combine like terms: -7.211102551 + 7 = -0.211102551 x = -0.211102551 Simplifying x = -0.211102551

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.211102551, -0.211102551}

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