2x(x-33)+x=162

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Solution for 2x(x-33)+x=162 equation:


Simplifying
2x(x + -33) + x = 162

Reorder the terms:
2x(-33 + x) + x = 162
(-33 * 2x + x * 2x) + x = 162
(-66x + 2x2) + x = 162

Reorder the terms:
-66x + x + 2x2 = 162

Combine like terms: -66x + x = -65x
-65x + 2x2 = 162

Solving
-65x + 2x2 = 162

Solving for variable 'x'.

Reorder the terms:
-162 + -65x + 2x2 = 162 + -162

Combine like terms: 162 + -162 = 0
-162 + -65x + 2x2 = 0

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

Divide each side by '2'.
-81 + -32.5x + x2 = 0

Move the constant term to the right:

Add '81' to each side of the equation.
-81 + -32.5x + 81 + x2 = 0 + 81

Reorder the terms:
-81 + 81 + -32.5x + x2 = 0 + 81

Combine like terms: -81 + 81 = 0
0 + -32.5x + x2 = 0 + 81
-32.5x + x2 = 0 + 81

Combine like terms: 0 + 81 = 81
-32.5x + x2 = 81

The x term is -32.5x.  Take half its coefficient (-16.25).
Square it (264.0625) and add it to both sides.

Add '264.0625' to each side of the equation.
-32.5x + 264.0625 + x2 = 81 + 264.0625

Reorder the terms:
264.0625 + -32.5x + x2 = 81 + 264.0625

Combine like terms: 81 + 264.0625 = 345.0625
264.0625 + -32.5x + x2 = 345.0625

Factor a perfect square on the left side:
(x + -16.25)(x + -16.25) = 345.0625

Calculate the square root of the right side: 18.575857988

Break this problem into two subproblems by setting 
(x + -16.25) equal to 18.575857988 and -18.575857988.

Subproblem 1

x + -16.25 = 18.575857988 Simplifying x + -16.25 = 18.575857988 Reorder the terms: -16.25 + x = 18.575857988 Solving -16.25 + x = 18.575857988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = 18.575857988 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = 18.575857988 + 16.25 x = 18.575857988 + 16.25 Combine like terms: 18.575857988 + 16.25 = 34.825857988 x = 34.825857988 Simplifying x = 34.825857988

Subproblem 2

x + -16.25 = -18.575857988 Simplifying x + -16.25 = -18.575857988 Reorder the terms: -16.25 + x = -18.575857988 Solving -16.25 + x = -18.575857988 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '16.25' to each side of the equation. -16.25 + 16.25 + x = -18.575857988 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + x = -18.575857988 + 16.25 x = -18.575857988 + 16.25 Combine like terms: -18.575857988 + 16.25 = -2.325857988 x = -2.325857988 Simplifying x = -2.325857988

Solution

The solution to the problem is based on the solutions from the subproblems. x = {34.825857988, -2.325857988}

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