0=x^2-14x-9

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Solution for 0=x^2-14x-9 equation:


Simplifying
0 = x2 + -14x + -9

Reorder the terms:
0 = -9 + -14x + x2

Solving
0 = -9 + -14x + x2

Solving for variable 'x'.

Combine like terms: 0 + 9 = 9
9 + 14x + -1x2 = -9 + -14x + x2 + 9 + 14x + -1x2

Reorder the terms:
9 + 14x + -1x2 = -9 + 9 + -14x + 14x + x2 + -1x2

Combine like terms: -9 + 9 = 0
9 + 14x + -1x2 = 0 + -14x + 14x + x2 + -1x2
9 + 14x + -1x2 = -14x + 14x + x2 + -1x2

Combine like terms: -14x + 14x = 0
9 + 14x + -1x2 = 0 + x2 + -1x2
9 + 14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
9 + 14x + -1x2 = 0

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

Divide each side by '-1'.
-9 + -14x + x2 = 0

Move the constant term to the right:

Add '9' to each side of the equation.
-9 + -14x + 9 + x2 = 0 + 9

Reorder the terms:
-9 + 9 + -14x + x2 = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -14x + x2 = 0 + 9
-14x + x2 = 0 + 9

Combine like terms: 0 + 9 = 9
-14x + x2 = 9

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 = 9 + 49

Reorder the terms:
49 + -14x + x2 = 9 + 49

Combine like terms: 9 + 49 = 58
49 + -14x + x2 = 58

Factor a perfect square on the left side:
(x + -7)(x + -7) = 58

Calculate the square root of the right side: 7.615773106

Break this problem into two subproblems by setting 
(x + -7) equal to 7.615773106 and -7.615773106.

Subproblem 1

x + -7 = 7.615773106 Simplifying x + -7 = 7.615773106 Reorder the terms: -7 + x = 7.615773106 Solving -7 + x = 7.615773106 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 = 7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + x = 7.615773106 + 7 x = 7.615773106 + 7 Combine like terms: 7.615773106 + 7 = 14.615773106 x = 14.615773106 Simplifying x = 14.615773106

Subproblem 2

x + -7 = -7.615773106 Simplifying x + -7 = -7.615773106 Reorder the terms: -7 + x = -7.615773106 Solving -7 + x = -7.615773106 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 = -7.615773106 + 7 Combine like terms: -7 + 7 = 0 0 + x = -7.615773106 + 7 x = -7.615773106 + 7 Combine like terms: -7.615773106 + 7 = -0.615773106 x = -0.615773106 Simplifying x = -0.615773106

Solution

The solution to the problem is based on the solutions from the subproblems. x = {14.615773106, -0.615773106}

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