x^2-7x-140=0

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Solution for x^2-7x-140=0 equation:


Simplifying
x2 + -7x + -140 = 0

Reorder the terms:
-140 + -7x + x2 = 0

Solving
-140 + -7x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '140' to each side of the equation.
-140 + -7x + 140 + x2 = 0 + 140

Reorder the terms:
-140 + 140 + -7x + x2 = 0 + 140

Combine like terms: -140 + 140 = 0
0 + -7x + x2 = 0 + 140
-7x + x2 = 0 + 140

Combine like terms: 0 + 140 = 140
-7x + x2 = 140

The x term is -7x.  Take half its coefficient (-3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
-7x + 12.25 + x2 = 140 + 12.25

Reorder the terms:
12.25 + -7x + x2 = 140 + 12.25

Combine like terms: 140 + 12.25 = 152.25
12.25 + -7x + x2 = 152.25

Factor a perfect square on the left side:
(x + -3.5)(x + -3.5) = 152.25

Calculate the square root of the right side: 12.338962679

Break this problem into two subproblems by setting 
(x + -3.5) equal to 12.338962679 and -12.338962679.


Subproblem 1
x + -3.5 = 12.338962679

Simplifying
x + -3.5 = 12.338962679

Reorder the terms:
-3.5 + x = 12.338962679

Solving
-3.5 + x = 12.338962679

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = 12.338962679 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = 12.338962679 + 3.5
x = 12.338962679 + 3.5

Combine like terms: 12.338962679 + 3.5 = 15.838962679
x = 15.838962679

Simplifying
x = 15.838962679


Subproblem 2
x + -3.5 = -12.338962679

Simplifying
x + -3.5 = -12.338962679

Reorder the terms:
-3.5 + x = -12.338962679

Solving
-3.5 + x = -12.338962679

Solving for variable 'x'.

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

Add '3.5' to each side of the equation.
-3.5 + 3.5 + x = -12.338962679 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + x = -12.338962679 + 3.5
x = -12.338962679 + 3.5

Combine like terms: -12.338962679 + 3.5 = -8.838962679
x = -8.838962679

Simplifying
x = -8.838962679


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {15.838962679, -8.838962679}

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