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

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


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

Combine like terms: 17 + 7 = 24
20x + (24) + 15x(12x + 17) = 360
20x + 24 + 15x(12x + 17) = 360

Reorder the terms:
20x + 24 + 15x(17 + 12x) = 360
20x + 24 + (17 * 15x + 12x * 15x) = 360
20x + 24 + (255x + 180x2) = 360

Reorder the terms:
24 + 20x + 255x + 180x2 = 360

Combine like terms: 20x + 255x = 275x
24 + 275x + 180x2 = 360

Solving
24 + 275x + 180x2 = 360

Solving for variable 'x'.

Reorder the terms:
24 + -360 + 275x + 180x2 = 360 + -360

Combine like terms: 24 + -360 = -336
-336 + 275x + 180x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-336 + 275x + 180x2 = 0

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

Divide each side by '180'.
-1.866666667 + 1.527777778x + x2 = 0.0

Move the constant term to the right:

Add '1.866666667' to each side of the equation.
-1.866666667 + 1.527777778x + 1.866666667 + x2 = 0.0 + 1.866666667

Reorder the terms:
-1.866666667 + 1.866666667 + 1.527777778x + x2 = 0.0 + 1.866666667

Combine like terms: -1.866666667 + 1.866666667 = 0.000000000
0.000000000 + 1.527777778x + x2 = 0.0 + 1.866666667
1.527777778x + x2 = 0.0 + 1.866666667

Combine like terms: 0.0 + 1.866666667 = 1.866666667
1.527777778x + x2 = 1.866666667

The x term is 1.527777778x.  Take half its coefficient (0.763888889).
Square it (0.5835262347) and add it to both sides.

Add '0.5835262347' to each side of the equation.
1.527777778x + 0.5835262347 + x2 = 1.866666667 + 0.5835262347

Reorder the terms:
0.5835262347 + 1.527777778x + x2 = 1.866666667 + 0.5835262347

Combine like terms: 1.866666667 + 0.5835262347 = 2.4501929017
0.5835262347 + 1.527777778x + x2 = 2.4501929017

Factor a perfect square on the left side:
(x + 0.763888889)(x + 0.763888889) = 2.4501929017

Calculate the square root of the right side: 1.565309203

Break this problem into two subproblems by setting 
(x + 0.763888889) equal to 1.565309203 and -1.565309203.

Subproblem 1

x + 0.763888889 = 1.565309203 Simplifying x + 0.763888889 = 1.565309203 Reorder the terms: 0.763888889 + x = 1.565309203 Solving 0.763888889 + x = 1.565309203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.763888889' to each side of the equation. 0.763888889 + -0.763888889 + x = 1.565309203 + -0.763888889 Combine like terms: 0.763888889 + -0.763888889 = 0.000000000 0.000000000 + x = 1.565309203 + -0.763888889 x = 1.565309203 + -0.763888889 Combine like terms: 1.565309203 + -0.763888889 = 0.801420314 x = 0.801420314 Simplifying x = 0.801420314

Subproblem 2

x + 0.763888889 = -1.565309203 Simplifying x + 0.763888889 = -1.565309203 Reorder the terms: 0.763888889 + x = -1.565309203 Solving 0.763888889 + x = -1.565309203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.763888889' to each side of the equation. 0.763888889 + -0.763888889 + x = -1.565309203 + -0.763888889 Combine like terms: 0.763888889 + -0.763888889 = 0.000000000 0.000000000 + x = -1.565309203 + -0.763888889 x = -1.565309203 + -0.763888889 Combine like terms: -1.565309203 + -0.763888889 = -2.329198092 x = -2.329198092 Simplifying x = -2.329198092

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.801420314, -2.329198092}

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