(17x-7)+20x+15x(12x-17)=360

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Solution for (17x-7)+20x+15x(12x-17)=360 equation:


Simplifying
(17x + -7) + 20x + 15x(12x + -17) = 360

Reorder the terms:
(-7 + 17x) + 20x + 15x(12x + -17) = 360

Remove parenthesis around (-7 + 17x)
-7 + 17x + 20x + 15x(12x + -17) = 360

Reorder the terms:
-7 + 17x + 20x + 15x(-17 + 12x) = 360
-7 + 17x + 20x + (-17 * 15x + 12x * 15x) = 360
-7 + 17x + 20x + (-255x + 180x2) = 360

Combine like terms: 17x + 20x = 37x
-7 + 37x + -255x + 180x2 = 360

Combine like terms: 37x + -255x = -218x
-7 + -218x + 180x2 = 360

Solving
-7 + -218x + 180x2 = 360

Solving for variable 'x'.

Reorder the terms:
-7 + -360 + -218x + 180x2 = 360 + -360

Combine like terms: -7 + -360 = -367
-367 + -218x + 180x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-367 + -218x + 180x2 = 0

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

Divide each side by '180'.
-2.038888889 + -1.211111111x + x2 = 0.0

Move the constant term to the right:

Add '2.038888889' to each side of the equation.
-2.038888889 + -1.211111111x + 2.038888889 + x2 = 0.0 + 2.038888889

Reorder the terms:
-2.038888889 + 2.038888889 + -1.211111111x + x2 = 0.0 + 2.038888889

Combine like terms: -2.038888889 + 2.038888889 = 0.000000000
0.000000000 + -1.211111111x + x2 = 0.0 + 2.038888889
-1.211111111x + x2 = 0.0 + 2.038888889

Combine like terms: 0.0 + 2.038888889 = 2.038888889
-1.211111111x + x2 = 2.038888889

The x term is -1.211111111x.  Take half its coefficient (-0.6055555555).
Square it (0.3666975308) and add it to both sides.

Add '0.3666975308' to each side of the equation.
-1.211111111x + 0.3666975308 + x2 = 2.038888889 + 0.3666975308

Reorder the terms:
0.3666975308 + -1.211111111x + x2 = 2.038888889 + 0.3666975308

Combine like terms: 2.038888889 + 0.3666975308 = 2.4055864198
0.3666975308 + -1.211111111x + x2 = 2.4055864198

Factor a perfect square on the left side:
(x + -0.6055555555)(x + -0.6055555555) = 2.4055864198

Calculate the square root of the right side: 1.5509953

Break this problem into two subproblems by setting 
(x + -0.6055555555) equal to 1.5509953 and -1.5509953.

Subproblem 1

x + -0.6055555555 = 1.5509953 Simplifying x + -0.6055555555 = 1.5509953 Reorder the terms: -0.6055555555 + x = 1.5509953 Solving -0.6055555555 + x = 1.5509953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6055555555' to each side of the equation. -0.6055555555 + 0.6055555555 + x = 1.5509953 + 0.6055555555 Combine like terms: -0.6055555555 + 0.6055555555 = 0.0000000000 0.0000000000 + x = 1.5509953 + 0.6055555555 x = 1.5509953 + 0.6055555555 Combine like terms: 1.5509953 + 0.6055555555 = 2.1565508555 x = 2.1565508555 Simplifying x = 2.1565508555

Subproblem 2

x + -0.6055555555 = -1.5509953 Simplifying x + -0.6055555555 = -1.5509953 Reorder the terms: -0.6055555555 + x = -1.5509953 Solving -0.6055555555 + x = -1.5509953 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.6055555555' to each side of the equation. -0.6055555555 + 0.6055555555 + x = -1.5509953 + 0.6055555555 Combine like terms: -0.6055555555 + 0.6055555555 = 0.0000000000 0.0000000000 + x = -1.5509953 + 0.6055555555 x = -1.5509953 + 0.6055555555 Combine like terms: -1.5509953 + 0.6055555555 = -0.9454397445 x = -0.9454397445 Simplifying x = -0.9454397445

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.1565508555, -0.9454397445}

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