0.2x+0.8x(50-x)=0.68(50)

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Solution for 0.2x+0.8x(50-x)=0.68(50) equation:


Simplifying
0.2x + 0.8x(50 + -1x) = 0.68(50)
0.2x + (50 * 0.8x + -1x * 0.8x) = 0.68(50)
0.2x + (40x + -0.8x2) = 0.68(50)

Combine like terms: 0.2x + 40x = 40.2x
40.2x + -0.8x2 = 0.68(50)

Multiply 0.68 * 50
40.2x + -0.8x2 = 34

Solving
40.2x + -0.8x2 = 34

Solving for variable 'x'.

Reorder the terms:
-34 + 40.2x + -0.8x2 = 34 + -34

Combine like terms: 34 + -34 = 0
-34 + 40.2x + -0.8x2 = 0

Begin completing the square.  Divide all terms by
-0.8 the coefficient of the squared term: 

Divide each side by '-0.8'.
42.5 + -50.25x + x2 = 0

Move the constant term to the right:

Add '-42.5' to each side of the equation.
42.5 + -50.25x + -42.5 + x2 = 0 + -42.5

Reorder the terms:
42.5 + -42.5 + -50.25x + x2 = 0 + -42.5

Combine like terms: 42.5 + -42.5 = 0.0
0.0 + -50.25x + x2 = 0 + -42.5
-50.25x + x2 = 0 + -42.5

Combine like terms: 0 + -42.5 = -42.5
-50.25x + x2 = -42.5

The x term is -50.25x.  Take half its coefficient (-25.125).
Square it (631.265625) and add it to both sides.

Add '631.265625' to each side of the equation.
-50.25x + 631.265625 + x2 = -42.5 + 631.265625

Reorder the terms:
631.265625 + -50.25x + x2 = -42.5 + 631.265625

Combine like terms: -42.5 + 631.265625 = 588.765625
631.265625 + -50.25x + x2 = 588.765625

Factor a perfect square on the left side:
(x + -25.125)(x + -25.125) = 588.765625

Calculate the square root of the right side: 24.264493092

Break this problem into two subproblems by setting 
(x + -25.125) equal to 24.264493092 and -24.264493092.

Subproblem 1

x + -25.125 = 24.264493092 Simplifying x + -25.125 = 24.264493092 Reorder the terms: -25.125 + x = 24.264493092 Solving -25.125 + x = 24.264493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.125' to each side of the equation. -25.125 + 25.125 + x = 24.264493092 + 25.125 Combine like terms: -25.125 + 25.125 = 0.000 0.000 + x = 24.264493092 + 25.125 x = 24.264493092 + 25.125 Combine like terms: 24.264493092 + 25.125 = 49.389493092 x = 49.389493092 Simplifying x = 49.389493092

Subproblem 2

x + -25.125 = -24.264493092 Simplifying x + -25.125 = -24.264493092 Reorder the terms: -25.125 + x = -24.264493092 Solving -25.125 + x = -24.264493092 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '25.125' to each side of the equation. -25.125 + 25.125 + x = -24.264493092 + 25.125 Combine like terms: -25.125 + 25.125 = 0.000 0.000 + x = -24.264493092 + 25.125 x = -24.264493092 + 25.125 Combine like terms: -24.264493092 + 25.125 = 0.860506908 x = 0.860506908 Simplifying x = 0.860506908

Solution

The solution to the problem is based on the solutions from the subproblems. x = {49.389493092, 0.860506908}

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