26.3=-0.004*x*x+x

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Solution for 26.3=-0.004*x*x+x equation:


Simplifying
26.3 = -0.004x * x + x

Multiply x * x
26.3 = -0.004x2 + x

Reorder the terms:
26.3 = x + -0.004x2

Solving
26.3 = x + -0.004x2

Solving for variable 'x'.

Reorder the terms:
26.3 + -1x + 0.004x2 = x + -1x + -0.004x2 + 0.004x2

Combine like terms: x + -1x = 0
26.3 + -1x + 0.004x2 = 0 + -0.004x2 + 0.004x2
26.3 + -1x + 0.004x2 = -0.004x2 + 0.004x2

Combine like terms: -0.004x2 + 0.004x2 = 0.000
26.3 + -1x + 0.004x2 = 0.000

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

Divide each side by '0.004'.
6575 + -250x + x2 = 0

Move the constant term to the right:

Add '-6575' to each side of the equation.
6575 + -250x + -6575 + x2 = 0 + -6575

Reorder the terms:
6575 + -6575 + -250x + x2 = 0 + -6575

Combine like terms: 6575 + -6575 = 0
0 + -250x + x2 = 0 + -6575
-250x + x2 = 0 + -6575

Combine like terms: 0 + -6575 = -6575
-250x + x2 = -6575

The x term is -250x.  Take half its coefficient (-125).
Square it (15625) and add it to both sides.

Add '15625' to each side of the equation.
-250x + 15625 + x2 = -6575 + 15625

Reorder the terms:
15625 + -250x + x2 = -6575 + 15625

Combine like terms: -6575 + 15625 = 9050
15625 + -250x + x2 = 9050

Factor a perfect square on the left side:
(x + -125)(x + -125) = 9050

Calculate the square root of the right side: 95.131487952

Break this problem into two subproblems by setting 
(x + -125) equal to 95.131487952 and -95.131487952.

Subproblem 1

x + -125 = 95.131487952 Simplifying x + -125 = 95.131487952 Reorder the terms: -125 + x = 95.131487952 Solving -125 + x = 95.131487952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = 95.131487952 + 125 Combine like terms: -125 + 125 = 0 0 + x = 95.131487952 + 125 x = 95.131487952 + 125 Combine like terms: 95.131487952 + 125 = 220.131487952 x = 220.131487952 Simplifying x = 220.131487952

Subproblem 2

x + -125 = -95.131487952 Simplifying x + -125 = -95.131487952 Reorder the terms: -125 + x = -95.131487952 Solving -125 + x = -95.131487952 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '125' to each side of the equation. -125 + 125 + x = -95.131487952 + 125 Combine like terms: -125 + 125 = 0 0 + x = -95.131487952 + 125 x = -95.131487952 + 125 Combine like terms: -95.131487952 + 125 = 29.868512048 x = 29.868512048 Simplifying x = 29.868512048

Solution

The solution to the problem is based on the solutions from the subproblems. x = {220.131487952, 29.868512048}

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