x^2-7x-7x+14-36=0

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Solution for x^2-7x-7x+14-36=0 equation:


Simplifying
x2 + -7x + -7x + 14 + -36 = 0

Reorder the terms:
14 + -36 + -7x + -7x + x2 = 0

Combine like terms: 14 + -36 = -22
-22 + -7x + -7x + x2 = 0

Combine like terms: -7x + -7x = -14x
-22 + -14x + x2 = 0

Solving
-22 + -14x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '22' to each side of the equation.
-22 + -14x + 22 + x2 = 0 + 22

Reorder the terms:
-22 + 22 + -14x + x2 = 0 + 22

Combine like terms: -22 + 22 = 0
0 + -14x + x2 = 0 + 22
-14x + x2 = 0 + 22

Combine like terms: 0 + 22 = 22
-14x + x2 = 22

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 = 22 + 49

Reorder the terms:
49 + -14x + x2 = 22 + 49

Combine like terms: 22 + 49 = 71
49 + -14x + x2 = 71

Factor a perfect square on the left side:
(x + -7)(x + -7) = 71

Calculate the square root of the right side: 8.426149773

Break this problem into two subproblems by setting 
(x + -7) equal to 8.426149773 and -8.426149773.

Subproblem 1

x + -7 = 8.426149773 Simplifying x + -7 = 8.426149773 Reorder the terms: -7 + x = 8.426149773 Solving -7 + x = 8.426149773 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 = 8.426149773 + 7 Combine like terms: -7 + 7 = 0 0 + x = 8.426149773 + 7 x = 8.426149773 + 7 Combine like terms: 8.426149773 + 7 = 15.426149773 x = 15.426149773 Simplifying x = 15.426149773

Subproblem 2

x + -7 = -8.426149773 Simplifying x + -7 = -8.426149773 Reorder the terms: -7 + x = -8.426149773 Solving -7 + x = -8.426149773 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 = -8.426149773 + 7 Combine like terms: -7 + 7 = 0 0 + x = -8.426149773 + 7 x = -8.426149773 + 7 Combine like terms: -8.426149773 + 7 = -1.426149773 x = -1.426149773 Simplifying x = -1.426149773

Solution

The solution to the problem is based on the solutions from the subproblems. x = {15.426149773, -1.426149773}

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