24=.0021x^2-0.286x+16.28

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Solution for 24=.0021x^2-0.286x+16.28 equation:


Simplifying
24 = 0.0021x2 + -0.286x + 16.28

Reorder the terms:
24 = 16.28 + -0.286x + 0.0021x2

Solving
24 = 16.28 + -0.286x + 0.0021x2

Solving for variable 'x'.

Combine like terms: 24 + -16.28 = 7.72
7.72 + 0.286x + -0.0021x2 = 16.28 + -0.286x + 0.0021x2 + -16.28 + 0.286x + -0.0021x2

Reorder the terms:
7.72 + 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
7.72 + 0.286x + -0.0021x2 = 0.00 + -0.286x + 0.286x + 0.0021x2 + -0.0021x2
7.72 + 0.286x + -0.0021x2 = -0.286x + 0.286x + 0.0021x2 + -0.0021x2

Combine like terms: -0.286x + 0.286x = 0.000
7.72 + 0.286x + -0.0021x2 = 0.000 + 0.0021x2 + -0.0021x2
7.72 + 0.286x + -0.0021x2 = 0.0021x2 + -0.0021x2

Combine like terms: 0.0021x2 + -0.0021x2 = 0.0000
7.72 + 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'.
-3676.190476 + -136.1904762x + x2 = 0

Move the constant term to the right:

Add '3676.190476' to each side of the equation.
-3676.190476 + -136.1904762x + 3676.190476 + x2 = 0 + 3676.190476

Reorder the terms:
-3676.190476 + 3676.190476 + -136.1904762x + x2 = 0 + 3676.190476

Combine like terms: -3676.190476 + 3676.190476 = 0.000000
0.000000 + -136.1904762x + x2 = 0 + 3676.190476
-136.1904762x + x2 = 0 + 3676.190476

Combine like terms: 0 + 3676.190476 = 3676.190476
-136.1904762x + x2 = 3676.190476

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 = 3676.190476 + 4636.961452

Reorder the terms:
4636.961452 + -136.1904762x + x2 = 3676.190476 + 4636.961452

Combine like terms: 3676.190476 + 4636.961452 = 8313.151928
4636.961452 + -136.1904762x + x2 = 8313.151928

Factor a perfect square on the left side:
(x + -68.0952381)(x + -68.0952381) = 8313.151928

Calculate the square root of the right side: 91.176487803

Break this problem into two subproblems by setting 
(x + -68.0952381) equal to 91.176487803 and -91.176487803.

Subproblem 1

x + -68.0952381 = 91.176487803 Simplifying x + -68.0952381 = 91.176487803 Reorder the terms: -68.0952381 + x = 91.176487803 Solving -68.0952381 + x = 91.176487803 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 = 91.176487803 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = 91.176487803 + 68.0952381 x = 91.176487803 + 68.0952381 Combine like terms: 91.176487803 + 68.0952381 = 159.271725903 x = 159.271725903 Simplifying x = 159.271725903

Subproblem 2

x + -68.0952381 = -91.176487803 Simplifying x + -68.0952381 = -91.176487803 Reorder the terms: -68.0952381 + x = -91.176487803 Solving -68.0952381 + x = -91.176487803 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 = -91.176487803 + 68.0952381 Combine like terms: -68.0952381 + 68.0952381 = 0.0000000 0.0000000 + x = -91.176487803 + 68.0952381 x = -91.176487803 + 68.0952381 Combine like terms: -91.176487803 + 68.0952381 = -23.081249703 x = -23.081249703 Simplifying x = -23.081249703

Solution

The solution to the problem is based on the solutions from the subproblems. x = {159.271725903, -23.081249703}

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