-840-140x+10x^2=0

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Solution for -840-140x+10x^2=0 equation: 


Simplifying
-840 + -140x + 10x2 = 0

Solving
-840 + -140x + 10x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '10'.
10(-84 + -14x + x2) = 0

Ignore the factor 10.

Subproblem 1
Set the factor '(-84 + -14x + x2)' equal to zero and attempt to solve:

Simplifying
-84 + -14x + x2 = 0

Solving
-84 + -14x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '84' to each side of the equation.
-84 + -14x + 84 + x2 = 0 + 84

Reorder the terms:
-84 + 84 + -14x + x2 = 0 + 84

Combine like terms: -84 + 84 = 0
0 + -14x + x2 = 0 + 84
-14x + x2 = 0 + 84

Combine like terms: 0 + 84 = 84
-14x + x2 = 84

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 = 84 + 49

Reorder the terms:
49 + -14x + x2 = 84 + 49

Combine like terms: 84 + 49 = 133
49 + -14x + x2 = 133

Factor a perfect square on the left side:
(x + -7)(x + -7) = 133

Calculate the square root of the right side: 11.532562595

Break this problem into two subproblems by setting 
(x + -7) equal to 11.532562595 and -11.532562595.


Subproblem 1
x + -7 = 11.532562595

Simplifying
x + -7 = 11.532562595

Reorder the terms:
-7 + x = 11.532562595

Solving
-7 + x = 11.532562595

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 = 11.532562595 + 7

Combine like terms: -7 + 7 = 0
0 + x = 11.532562595 + 7
x = 11.532562595 + 7

Combine like terms: 11.532562595 + 7 = 18.532562595
x = 18.532562595

Simplifying
x = 18.532562595


Subproblem 2
x + -7 = -11.532562595

Simplifying
x + -7 = -11.532562595

Reorder the terms:
-7 + x = -11.532562595

Solving
-7 + x = -11.532562595

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 = -11.532562595 + 7

Combine like terms: -7 + 7 = 0
0 + x = -11.532562595 + 7
x = -11.532562595 + 7

Combine like terms: -11.532562595 + 7 = -4.532562595
x = -4.532562595

Simplifying
x = -4.532562595


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {18.532562595, -4.532562595}
Solution
x = {18.532562595, -4.532562595}

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