90+(3x+5)x+2x=180

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Solution for 90+(3x+5)x+2x=180 equation:


Simplifying
90 + (3x + 5) * x + 2x = 180

Reorder the terms:
90 + (5 + 3x) * x + 2x = 180

Reorder the terms for easier multiplication:
90 + x(5 + 3x) + 2x = 180
90 + (5 * x + 3x * x) + 2x = 180
90 + (5x + 3x2) + 2x = 180

Reorder the terms:
90 + 5x + 2x + 3x2 = 180

Combine like terms: 5x + 2x = 7x
90 + 7x + 3x2 = 180

Solving
90 + 7x + 3x2 = 180

Solving for variable 'x'.

Reorder the terms:
90 + -180 + 7x + 3x2 = 180 + -180

Combine like terms: 90 + -180 = -90
-90 + 7x + 3x2 = 180 + -180

Combine like terms: 180 + -180 = 0
-90 + 7x + 3x2 = 0

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

Divide each side by '3'.
-30 + 2.333333333x + x2 = 0

Move the constant term to the right:

Add '30' to each side of the equation.
-30 + 2.333333333x + 30 + x2 = 0 + 30

Reorder the terms:
-30 + 30 + 2.333333333x + x2 = 0 + 30

Combine like terms: -30 + 30 = 0
0 + 2.333333333x + x2 = 0 + 30
2.333333333x + x2 = 0 + 30

Combine like terms: 0 + 30 = 30
2.333333333x + x2 = 30

The x term is 2.333333333x.  Take half its coefficient (1.166666667).
Square it (1.361111112) and add it to both sides.

Add '1.361111112' to each side of the equation.
2.333333333x + 1.361111112 + x2 = 30 + 1.361111112

Reorder the terms:
1.361111112 + 2.333333333x + x2 = 30 + 1.361111112

Combine like terms: 30 + 1.361111112 = 31.361111112
1.361111112 + 2.333333333x + x2 = 31.361111112

Factor a perfect square on the left side:
(x + 1.166666667)(x + 1.166666667) = 31.361111112

Calculate the square root of the right side: 5.600099206

Break this problem into two subproblems by setting 
(x + 1.166666667) equal to 5.600099206 and -5.600099206.

Subproblem 1

x + 1.166666667 = 5.600099206 Simplifying x + 1.166666667 = 5.600099206 Reorder the terms: 1.166666667 + x = 5.600099206 Solving 1.166666667 + x = 5.600099206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = 5.600099206 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = 5.600099206 + -1.166666667 x = 5.600099206 + -1.166666667 Combine like terms: 5.600099206 + -1.166666667 = 4.433432539 x = 4.433432539 Simplifying x = 4.433432539

Subproblem 2

x + 1.166666667 = -5.600099206 Simplifying x + 1.166666667 = -5.600099206 Reorder the terms: 1.166666667 + x = -5.600099206 Solving 1.166666667 + x = -5.600099206 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.166666667' to each side of the equation. 1.166666667 + -1.166666667 + x = -5.600099206 + -1.166666667 Combine like terms: 1.166666667 + -1.166666667 = 0.000000000 0.000000000 + x = -5.600099206 + -1.166666667 x = -5.600099206 + -1.166666667 Combine like terms: -5.600099206 + -1.166666667 = -6.766765873 x = -6.766765873 Simplifying x = -6.766765873

Solution

The solution to the problem is based on the solutions from the subproblems. x = {4.433432539, -6.766765873}

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