28=0.001(0.732x^2+15.417x+605.738)

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Solution for 28=0.001(0.732x^2+15.417x+605.738) equation:


Simplifying
28 = 0.001(0.732x2 + 15.417x + 605.738)

Reorder the terms:
28 = 0.001(605.738 + 15.417x + 0.732x2)
28 = (605.738 * 0.001 + 15.417x * 0.001 + 0.732x2 * 0.001)
28 = (0.605738 + 0.015417x + 0.000732x2)

Solving
28 = 0.605738 + 0.015417x + 0.000732x2

Solving for variable 'x'.

Combine like terms: 28 + -0.605738 = 27.394262
27.394262 + -0.015417x + -0.000732x2 = 0.605738 + 0.015417x + 0.000732x2 + -0.605738 + -0.015417x + -0.000732x2

Reorder the terms:
27.394262 + -0.015417x + -0.000732x2 = 0.605738 + -0.605738 + 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2

Combine like terms: 0.605738 + -0.605738 = 0.000000
27.394262 + -0.015417x + -0.000732x2 = 0.000000 + 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2
27.394262 + -0.015417x + -0.000732x2 = 0.015417x + -0.015417x + 0.000732x2 + -0.000732x2

Combine like terms: 0.015417x + -0.015417x = 0.000000
27.394262 + -0.015417x + -0.000732x2 = 0.000000 + 0.000732x2 + -0.000732x2
27.394262 + -0.015417x + -0.000732x2 = 0.000732x2 + -0.000732x2

Combine like terms: 0.000732x2 + -0.000732x2 = 0.000000
27.394262 + -0.015417x + -0.000732x2 = 0.000000

Begin completing the square.  Divide all terms by
-0.000732 the coefficient of the squared term: 

Divide each side by '-0.000732'.
-37423.85519 + 21.06147541x + x2 = 0

Move the constant term to the right:

Add '37423.85519' to each side of the equation.
-37423.85519 + 21.06147541x + 37423.85519 + x2 = 0 + 37423.85519

Reorder the terms:
-37423.85519 + 37423.85519 + 21.06147541x + x2 = 0 + 37423.85519

Combine like terms: -37423.85519 + 37423.85519 = 0.00000
0.00000 + 21.06147541x + x2 = 0 + 37423.85519
21.06147541x + x2 = 0 + 37423.85519

Combine like terms: 0 + 37423.85519 = 37423.85519
21.06147541x + x2 = 37423.85519

The x term is 21.06147541x.  Take half its coefficient (10.53073771).
Square it (110.8964367) and add it to both sides.

Add '110.8964367' to each side of the equation.
21.06147541x + 110.8964367 + x2 = 37423.85519 + 110.8964367

Reorder the terms:
110.8964367 + 21.06147541x + x2 = 37423.85519 + 110.8964367

Combine like terms: 37423.85519 + 110.8964367 = 37534.7516267
110.8964367 + 21.06147541x + x2 = 37534.7516267

Factor a perfect square on the left side:
(x + 10.53073771)(x + 10.53073771) = 37534.7516267

Calculate the square root of the right side: 193.738874846

Break this problem into two subproblems by setting 
(x + 10.53073771) equal to 193.738874846 and -193.738874846.

Subproblem 1

x + 10.53073771 = 193.738874846 Simplifying x + 10.53073771 = 193.738874846 Reorder the terms: 10.53073771 + x = 193.738874846 Solving 10.53073771 + x = 193.738874846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.53073771' to each side of the equation. 10.53073771 + -10.53073771 + x = 193.738874846 + -10.53073771 Combine like terms: 10.53073771 + -10.53073771 = 0.00000000 0.00000000 + x = 193.738874846 + -10.53073771 x = 193.738874846 + -10.53073771 Combine like terms: 193.738874846 + -10.53073771 = 183.208137136 x = 183.208137136 Simplifying x = 183.208137136

Subproblem 2

x + 10.53073771 = -193.738874846 Simplifying x + 10.53073771 = -193.738874846 Reorder the terms: 10.53073771 + x = -193.738874846 Solving 10.53073771 + x = -193.738874846 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.53073771' to each side of the equation. 10.53073771 + -10.53073771 + x = -193.738874846 + -10.53073771 Combine like terms: 10.53073771 + -10.53073771 = 0.00000000 0.00000000 + x = -193.738874846 + -10.53073771 x = -193.738874846 + -10.53073771 Combine like terms: -193.738874846 + -10.53073771 = -204.269612556 x = -204.269612556 Simplifying x = -204.269612556

Solution

The solution to the problem is based on the solutions from the subproblems. x = {183.208137136, -204.269612556}

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