0=8-.14x-.003x^2

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Solution for 0=8-.14x-.003x^2 equation:


Simplifying
0 = 8 + -0.14x + -0.003x2

Solving
0 = 8 + -0.14x + -0.003x2

Solving for variable 'x'.

Combine like terms: 0 + -8 = -8
-8 + 0.14x + 0.003x2 = 8 + -0.14x + -0.003x2 + -8 + 0.14x + 0.003x2

Reorder the terms:
-8 + 0.14x + 0.003x2 = 8 + -8 + -0.14x + 0.14x + -0.003x2 + 0.003x2

Combine like terms: 8 + -8 = 0
-8 + 0.14x + 0.003x2 = 0 + -0.14x + 0.14x + -0.003x2 + 0.003x2
-8 + 0.14x + 0.003x2 = -0.14x + 0.14x + -0.003x2 + 0.003x2

Combine like terms: -0.14x + 0.14x = 0.00
-8 + 0.14x + 0.003x2 = 0.00 + -0.003x2 + 0.003x2
-8 + 0.14x + 0.003x2 = -0.003x2 + 0.003x2

Combine like terms: -0.003x2 + 0.003x2 = 0.000
-8 + 0.14x + 0.003x2 = 0.000

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

Divide each side by '0.003'.
-2666.666667 + 46.66666667x + x2 = 0

Move the constant term to the right:

Add '2666.666667' to each side of the equation.
-2666.666667 + 46.66666667x + 2666.666667 + x2 = 0 + 2666.666667

Reorder the terms:
-2666.666667 + 2666.666667 + 46.66666667x + x2 = 0 + 2666.666667

Combine like terms: -2666.666667 + 2666.666667 = 0.000000
0.000000 + 46.66666667x + x2 = 0 + 2666.666667
46.66666667x + x2 = 0 + 2666.666667

Combine like terms: 0 + 2666.666667 = 2666.666667
46.66666667x + x2 = 2666.666667

The x term is 46.66666667x.  Take half its coefficient (23.33333334).
Square it (544.4444448) and add it to both sides.

Add '544.4444448' to each side of the equation.
46.66666667x + 544.4444448 + x2 = 2666.666667 + 544.4444448

Reorder the terms:
544.4444448 + 46.66666667x + x2 = 2666.666667 + 544.4444448

Combine like terms: 2666.666667 + 544.4444448 = 3211.1111118
544.4444448 + 46.66666667x + x2 = 3211.1111118

Factor a perfect square on the left side:
(x + 23.33333334)(x + 23.33333334) = 3211.1111118

Calculate the square root of the right side: 56.666666673

Break this problem into two subproblems by setting 
(x + 23.33333334) equal to 56.666666673 and -56.666666673.

Subproblem 1

x + 23.33333334 = 56.666666673 Simplifying x + 23.33333334 = 56.666666673 Reorder the terms: 23.33333334 + x = 56.666666673 Solving 23.33333334 + x = 56.666666673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.33333334' to each side of the equation. 23.33333334 + -23.33333334 + x = 56.666666673 + -23.33333334 Combine like terms: 23.33333334 + -23.33333334 = 0.00000000 0.00000000 + x = 56.666666673 + -23.33333334 x = 56.666666673 + -23.33333334 Combine like terms: 56.666666673 + -23.33333334 = 33.333333333 x = 33.333333333 Simplifying x = 33.333333333

Subproblem 2

x + 23.33333334 = -56.666666673 Simplifying x + 23.33333334 = -56.666666673 Reorder the terms: 23.33333334 + x = -56.666666673 Solving 23.33333334 + x = -56.666666673 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-23.33333334' to each side of the equation. 23.33333334 + -23.33333334 + x = -56.666666673 + -23.33333334 Combine like terms: 23.33333334 + -23.33333334 = 0.00000000 0.00000000 + x = -56.666666673 + -23.33333334 x = -56.666666673 + -23.33333334 Combine like terms: -56.666666673 + -23.33333334 = -80.000000013 x = -80.000000013 Simplifying x = -80.000000013

Solution

The solution to the problem is based on the solutions from the subproblems. x = {33.333333333, -80.000000013}

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