120x-66+789x(32-66+x+59x-2)-(7)(7)=30+x-22x+66

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Solution for 120x-66+789x(32-66+x+59x-2)-(7)(7)=30+x-22x+66 equation:


Simplifying
120x + -66 + 789x(32 + -66 + x + 59x + -2) + -1(7)(7) = 30 + x + -22x + 66

Reorder the terms:
120x + -66 + 789x(32 + -66 + -2 + x + 59x) + -1(7)(7) = 30 + x + -22x + 66

Combine like terms: 32 + -66 = -34
120x + -66 + 789x(-34 + -2 + x + 59x) + -1(7)(7) = 30 + x + -22x + 66

Combine like terms: -34 + -2 = -36
120x + -66 + 789x(-36 + x + 59x) + -1(7)(7) = 30 + x + -22x + 66

Combine like terms: x + 59x = 60x
120x + -66 + 789x(-36 + 60x) + -1(7)(7) = 30 + x + -22x + 66
120x + -66 + (-36 * 789x + 60x * 789x) + -1(7)(7) = 30 + x + -22x + 66
120x + -66 + (-28404x + 47340x2) + -1(7)(7) = 30 + x + -22x + 66

Multiply -1 * 7
120x + -66 + -28404x + 47340x2 + -7 * 7 = 30 + x + -22x + 66

Multiply -7 * 7
120x + -66 + -28404x + 47340x2 + -49 = 30 + x + -22x + 66

Reorder the terms:
-66 + -49 + 120x + -28404x + 47340x2 = 30 + x + -22x + 66

Combine like terms: -66 + -49 = -115
-115 + 120x + -28404x + 47340x2 = 30 + x + -22x + 66

Combine like terms: 120x + -28404x = -28284x
-115 + -28284x + 47340x2 = 30 + x + -22x + 66

Reorder the terms:
-115 + -28284x + 47340x2 = 30 + 66 + x + -22x

Combine like terms: 30 + 66 = 96
-115 + -28284x + 47340x2 = 96 + x + -22x

Combine like terms: x + -22x = -21x
-115 + -28284x + 47340x2 = 96 + -21x

Solving
-115 + -28284x + 47340x2 = 96 + -21x

Solving for variable 'x'.

Reorder the terms:
-115 + -96 + -28284x + 21x + 47340x2 = 96 + -21x + -96 + 21x

Combine like terms: -115 + -96 = -211
-211 + -28284x + 21x + 47340x2 = 96 + -21x + -96 + 21x

Combine like terms: -28284x + 21x = -28263x
-211 + -28263x + 47340x2 = 96 + -21x + -96 + 21x

Reorder the terms:
-211 + -28263x + 47340x2 = 96 + -96 + -21x + 21x

Combine like terms: 96 + -96 = 0
-211 + -28263x + 47340x2 = 0 + -21x + 21x
-211 + -28263x + 47340x2 = -21x + 21x

Combine like terms: -21x + 21x = 0
-211 + -28263x + 47340x2 = 0

Begin completing the square.  Divide all terms by
47340 the coefficient of the squared term: 

Divide each side by '47340'.
-0.004457118716 + -0.5970215463x + x2 = 0.0

Move the constant term to the right:

Add '0.004457118716' to each side of the equation.
-0.004457118716 + -0.5970215463x + 0.004457118716 + x2 = 0.0 + 0.004457118716

Reorder the terms:
-0.004457118716 + 0.004457118716 + -0.5970215463x + x2 = 0.0 + 0.004457118716

Combine like terms: -0.004457118716 + 0.004457118716 = 0.000000000000
0.000000000000 + -0.5970215463x + x2 = 0.0 + 0.004457118716
-0.5970215463x + x2 = 0.0 + 0.004457118716

Combine like terms: 0.0 + 0.004457118716 = 0.004457118716
-0.5970215463x + x2 = 0.004457118716

The x term is -0.5970215463x.  Take half its coefficient (-0.2985107732).
Square it (0.08910868172) and add it to both sides.

Add '0.08910868172' to each side of the equation.
-0.5970215463x + 0.08910868172 + x2 = 0.004457118716 + 0.08910868172

Reorder the terms:
0.08910868172 + -0.5970215463x + x2 = 0.004457118716 + 0.08910868172

Combine like terms: 0.004457118716 + 0.08910868172 = 0.093565800436
0.08910868172 + -0.5970215463x + x2 = 0.093565800436

Factor a perfect square on the left side:
(x + -0.2985107732)(x + -0.2985107732) = 0.093565800436

Calculate the square root of the right side: 0.305885273

Break this problem into two subproblems by setting 
(x + -0.2985107732) equal to 0.305885273 and -0.305885273.

Subproblem 1

x + -0.2985107732 = 0.305885273 Simplifying x + -0.2985107732 = 0.305885273 Reorder the terms: -0.2985107732 + x = 0.305885273 Solving -0.2985107732 + x = 0.305885273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2985107732' to each side of the equation. -0.2985107732 + 0.2985107732 + x = 0.305885273 + 0.2985107732 Combine like terms: -0.2985107732 + 0.2985107732 = 0.0000000000 0.0000000000 + x = 0.305885273 + 0.2985107732 x = 0.305885273 + 0.2985107732 Combine like terms: 0.305885273 + 0.2985107732 = 0.6043960462 x = 0.6043960462 Simplifying x = 0.6043960462

Subproblem 2

x + -0.2985107732 = -0.305885273 Simplifying x + -0.2985107732 = -0.305885273 Reorder the terms: -0.2985107732 + x = -0.305885273 Solving -0.2985107732 + x = -0.305885273 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2985107732' to each side of the equation. -0.2985107732 + 0.2985107732 + x = -0.305885273 + 0.2985107732 Combine like terms: -0.2985107732 + 0.2985107732 = 0.0000000000 0.0000000000 + x = -0.305885273 + 0.2985107732 x = -0.305885273 + 0.2985107732 Combine like terms: -0.305885273 + 0.2985107732 = -0.0073744998 x = -0.0073744998 Simplifying x = -0.0073744998

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.6043960462, -0.0073744998}

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