17x*3x=x-3+49

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Solution for 17x*3x=x-3+49 equation:


Simplifying
17x * 3x = x + -3 + 49

Reorder the terms for easier multiplication:
17 * 3x * x = x + -3 + 49

Multiply 17 * 3
51x * x = x + -3 + 49

Multiply x * x
51x2 = x + -3 + 49

Reorder the terms:
51x2 = -3 + 49 + x

Combine like terms: -3 + 49 = 46
51x2 = 46 + x

Solving
51x2 = 46 + x

Solving for variable 'x'.

Reorder the terms:
-46 + -1x + 51x2 = 46 + x + -46 + -1x

Reorder the terms:
-46 + -1x + 51x2 = 46 + -46 + x + -1x

Combine like terms: 46 + -46 = 0
-46 + -1x + 51x2 = 0 + x + -1x
-46 + -1x + 51x2 = x + -1x

Combine like terms: x + -1x = 0
-46 + -1x + 51x2 = 0

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

Divide each side by '51'.
-0.9019607843 + -0.01960784314x + x2 = 0

Move the constant term to the right:

Add '0.9019607843' to each side of the equation.
-0.9019607843 + -0.01960784314x + 0.9019607843 + x2 = 0 + 0.9019607843

Reorder the terms:
-0.9019607843 + 0.9019607843 + -0.01960784314x + x2 = 0 + 0.9019607843

Combine like terms: -0.9019607843 + 0.9019607843 = 0.0000000000
0.0000000000 + -0.01960784314x + x2 = 0 + 0.9019607843
-0.01960784314x + x2 = 0 + 0.9019607843

Combine like terms: 0 + 0.9019607843 = 0.9019607843
-0.01960784314x + x2 = 0.9019607843

The x term is -0.01960784314x.  Take half its coefficient (-0.00980392157).
Square it (0.00009611687815) and add it to both sides.

Add '0.00009611687815' to each side of the equation.
-0.01960784314x + 0.00009611687815 + x2 = 0.9019607843 + 0.00009611687815

Reorder the terms:
0.00009611687815 + -0.01960784314x + x2 = 0.9019607843 + 0.00009611687815

Combine like terms: 0.9019607843 + 0.00009611687815 = 0.90205690117815
0.00009611687815 + -0.01960784314x + x2 = 0.90205690117815

Factor a perfect square on the left side:
(x + -0.00980392157)(x + -0.00980392157) = 0.90205690117815

Calculate the square root of the right side: 0.949766761

Break this problem into two subproblems by setting 
(x + -0.00980392157) equal to 0.949766761 and -0.949766761.

Subproblem 1

x + -0.00980392157 = 0.949766761 Simplifying x + -0.00980392157 = 0.949766761 Reorder the terms: -0.00980392157 + x = 0.949766761 Solving -0.00980392157 + x = 0.949766761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00980392157' to each side of the equation. -0.00980392157 + 0.00980392157 + x = 0.949766761 + 0.00980392157 Combine like terms: -0.00980392157 + 0.00980392157 = 0.00000000000 0.00000000000 + x = 0.949766761 + 0.00980392157 x = 0.949766761 + 0.00980392157 Combine like terms: 0.949766761 + 0.00980392157 = 0.95957068257 x = 0.95957068257 Simplifying x = 0.95957068257

Subproblem 2

x + -0.00980392157 = -0.949766761 Simplifying x + -0.00980392157 = -0.949766761 Reorder the terms: -0.00980392157 + x = -0.949766761 Solving -0.00980392157 + x = -0.949766761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.00980392157' to each side of the equation. -0.00980392157 + 0.00980392157 + x = -0.949766761 + 0.00980392157 Combine like terms: -0.00980392157 + 0.00980392157 = 0.00000000000 0.00000000000 + x = -0.949766761 + 0.00980392157 x = -0.949766761 + 0.00980392157 Combine like terms: -0.949766761 + 0.00980392157 = -0.93996283943 x = -0.93996283943 Simplifying x = -0.93996283943

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.95957068257, -0.93996283943}

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