7.857x^2-35.382x+3.229=0

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Solution for 7.857x^2-35.382x+3.229=0 equation:


Simplifying
7.857x2 + -35.382x + 3.229 = 0

Reorder the terms:
3.229 + -35.382x + 7.857x2 = 0

Solving
3.229 + -35.382x + 7.857x2 = 0

Solving for variable 'x'.

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

Divide each side by '7.857'.
0.4109711086 + -4.503245514x + x2 = 0

Move the constant term to the right:

Add '-0.4109711086' to each side of the equation.
0.4109711086 + -4.503245514x + -0.4109711086 + x2 = 0 + -0.4109711086

Reorder the terms:
0.4109711086 + -0.4109711086 + -4.503245514x + x2 = 0 + -0.4109711086

Combine like terms: 0.4109711086 + -0.4109711086 = 0.0000000000
0.0000000000 + -4.503245514x + x2 = 0 + -0.4109711086
-4.503245514x + x2 = 0 + -0.4109711086

Combine like terms: 0 + -0.4109711086 = -0.4109711086
-4.503245514x + x2 = -0.4109711086

The x term is -4.503245514x.  Take half its coefficient (-2.251622757).
Square it (5.069805040) and add it to both sides.

Add '5.069805040' to each side of the equation.
-4.503245514x + 5.069805040 + x2 = -0.4109711086 + 5.069805040

Reorder the terms:
5.069805040 + -4.503245514x + x2 = -0.4109711086 + 5.069805040

Combine like terms: -0.4109711086 + 5.069805040 = 4.6588339314
5.069805040 + -4.503245514x + x2 = 4.6588339314

Factor a perfect square on the left side:
(x + -2.251622757)(x + -2.251622757) = 4.6588339314

Calculate the square root of the right side: 2.158433212

Break this problem into two subproblems by setting 
(x + -2.251622757) equal to 2.158433212 and -2.158433212.

Subproblem 1

x + -2.251622757 = 2.158433212 Simplifying x + -2.251622757 = 2.158433212 Reorder the terms: -2.251622757 + x = 2.158433212 Solving -2.251622757 + x = 2.158433212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.251622757' to each side of the equation. -2.251622757 + 2.251622757 + x = 2.158433212 + 2.251622757 Combine like terms: -2.251622757 + 2.251622757 = 0.000000000 0.000000000 + x = 2.158433212 + 2.251622757 x = 2.158433212 + 2.251622757 Combine like terms: 2.158433212 + 2.251622757 = 4.410055969 x = 4.410055969 Simplifying x = 4.410055969

Subproblem 2

x + -2.251622757 = -2.158433212 Simplifying x + -2.251622757 = -2.158433212 Reorder the terms: -2.251622757 + x = -2.158433212 Solving -2.251622757 + x = -2.158433212 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.251622757' to each side of the equation. -2.251622757 + 2.251622757 + x = -2.158433212 + 2.251622757 Combine like terms: -2.251622757 + 2.251622757 = 0.000000000 0.000000000 + x = -2.158433212 + 2.251622757 x = -2.158433212 + 2.251622757 Combine like terms: -2.158433212 + 2.251622757 = 0.093189545 x = 0.093189545 Simplifying x = 0.093189545

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.410055969, 0.093189545}

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