25=0.0021x^2-.286x+16.28

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Solution for 25=0.0021x^2-.286x+16.28 equation:


Simplifying
25 = 0.0021x2 + -0.286x + 16.28

Reorder the terms:
25 = 16.28 + -0.286x + 0.0021x2

Solving
25 = 16.28 + -0.286x + 0.0021x2

Solving for variable 'x'.

Combine like terms: 25 + -16.28 = 8.72
8.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2

Reorder the terms:
8.72 + 0.286x + -0.0021x2 = 16.28 + -16.28 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2

Combine like terms: 16.28 + -16.28 = 0.00
8.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2
8.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2

Combine like terms: -0.286x + 0.286x = 0.000
8.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2
8.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2

Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000
8.72 + 0.286x + -0.0021x2 = 0.0000

Begin completing the square.  Divide all terms by
-0.0021 the coefficient of the squared term: 

Divide each side by '-0.0021'.
-4152.380952 + -136.1904762x + x2 = 0

Move the constant term to the right:

Add '4152.380952' to each side of the equation.
-4152.380952 + -136.1904762x + 4152.380952 + x2 = 0 + 4152.380952

Reorder the terms:
-4152.380952 + 4152.380952 + -136.1904762x + x2 = 0 + 4152.380952

Combine like terms: -4152.380952 + 4152.380952 = 0.000000
0.000000 + -136.1904762x + x2 = 0 + 4152.380952
-136.1904762x + x2 = 0 + 4152.380952

Combine like terms: 0 + 4152.380952 = 4152.380952
-136.1904762x + x2 = 4152.380952

The x term is -136.1904762x.  Take half its coefficient (-68.0952381).
Square it (4636.961452) and add it to both sides.

Add '4636.961452' to each side of the equation.
-136.1904762x + 4636.961452 + x2 = 4152.380952 + 4636.961452

Reorder the terms:
4636.961452 + -136.1904762x + x2 = 4152.380952 + 4636.961452

Combine like terms: 4152.380952 + 4636.961452 = 8789.342404
4636.961452 + -136.1904762x + x2 = 8789.342404

Factor a perfect square on the left side:
(x + -68.0952381)(x + -68.0952381) = 8789.342404

Calculate the square root of the right side: 93.751492809

Break this problem into two subproblems by setting 
(x + -68.0952381) equal to 93.751492809 and -93.751492809.

Subproblem 1

x + -68.0952381 = 93.751492809 Simplifying x + -68.0952381 = 93.751492809 Reorder the terms: -68.0952381 + x = 93.751492809 Solving -68.0952381 + x = 93.751492809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.0952381' to each side of the equation. -68.0952381 + 68.0952381 + x = 93.751492809 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 93.751492809 + 68.0952381 x = 93.751492809 + 68.0952381 Combine like terms: 93.751492809 + 68.0952381 = 161.846730909 x = 161.846730909 Simplifying x = 161.846730909

Subproblem 2

x + -68.0952381 = -93.751492809 Simplifying x + -68.0952381 = -93.751492809 Reorder the terms: -68.0952381 + x = -93.751492809 Solving -68.0952381 + x = -93.751492809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '68.0952381' to each side of the equation. -68.0952381 + 68.0952381 + x = -93.751492809 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -93.751492809 + 68.0952381 x = -93.751492809 + 68.0952381 Combine like terms: -93.751492809 + 68.0952381 = -25.656254709 x = -25.656254709 Simplifying x = -25.656254709

Solution

The solution to the problem is based on the solutions from the subproblems. x = {161.846730909, -25.656254709}

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