0=x^2+14x-105

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Solution for 0=x^2+14x-105 equation:


Simplifying
0 = x2 + 14x + -105

Reorder the terms:
0 = -105 + 14x + x2

Solving
0 = -105 + 14x + x2

Solving for variable 'x'.

Combine like terms: 0 + 105 = 105
105 + -14x + -1x2 = -105 + 14x + x2 + 105 + -14x + -1x2

Reorder the terms:
105 + -14x + -1x2 = -105 + 105 + 14x + -14x + x2 + -1x2

Combine like terms: -105 + 105 = 0
105 + -14x + -1x2 = 0 + 14x + -14x + x2 + -1x2
105 + -14x + -1x2 = 14x + -14x + x2 + -1x2

Combine like terms: 14x + -14x = 0
105 + -14x + -1x2 = 0 + x2 + -1x2
105 + -14x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
105 + -14x + -1x2 = 0

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

Divide each side by '-1'.
-105 + 14x + x2 = 0

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + 14x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + 14x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + 14x + x2 = 0 + 105
14x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
14x + x2 = 105

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 = 105 + 49

Reorder the terms:
49 + 14x + x2 = 105 + 49

Combine like terms: 105 + 49 = 154
49 + 14x + x2 = 154

Factor a perfect square on the left side:
(x + 7)(x + 7) = 154

Calculate the square root of the right side: 12.409673646

Break this problem into two subproblems by setting 
(x + 7) equal to 12.409673646 and -12.409673646.

Subproblem 1

x + 7 = 12.409673646 Simplifying x + 7 = 12.409673646 Reorder the terms: 7 + x = 12.409673646 Solving 7 + x = 12.409673646 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 = 12.409673646 + -7 Combine like terms: 7 + -7 = 0 0 + x = 12.409673646 + -7 x = 12.409673646 + -7 Combine like terms: 12.409673646 + -7 = 5.409673646 x = 5.409673646 Simplifying x = 5.409673646

Subproblem 2

x + 7 = -12.409673646 Simplifying x + 7 = -12.409673646 Reorder the terms: 7 + x = -12.409673646 Solving 7 + x = -12.409673646 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 = -12.409673646 + -7 Combine like terms: 7 + -7 = 0 0 + x = -12.409673646 + -7 x = -12.409673646 + -7 Combine like terms: -12.409673646 + -7 = -19.409673646 x = -19.409673646 Simplifying x = -19.409673646

Solution

The solution to the problem is based on the solutions from the subproblems. x = {5.409673646, -19.409673646}

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