274=(220-x)1.50x+80x

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Solution for 274=(220-x)1.50x+80x equation:


Simplifying
274 = (220 + -1x) * 1.50x + 80x

Reorder the terms for easier multiplication:
274 = 1.50x(220 + -1x) + 80x
274 = (220 * 1.50x + -1x * 1.50x) + 80x
274 = (330x + -1.5x2) + 80x

Reorder the terms:
274 = 330x + 80x + -1.5x2

Combine like terms: 330x + 80x = 410x
274 = 410x + -1.5x2

Solving
274 = 410x + -1.5x2

Solving for variable 'x'.

Reorder the terms:
274 + -410x + 1.5x2 = 410x + -410x + -1.5x2 + 1.5x2

Combine like terms: 410x + -410x = 0
274 + -410x + 1.5x2 = 0 + -1.5x2 + 1.5x2
274 + -410x + 1.5x2 = -1.5x2 + 1.5x2

Combine like terms: -1.5x2 + 1.5x2 = 0.0
274 + -410x + 1.5x2 = 0.0

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

Divide each side by '1.5'.
182.6666667 + -273.3333333x + x2 = 0

Move the constant term to the right:

Add '-182.6666667' to each side of the equation.
182.6666667 + -273.3333333x + -182.6666667 + x2 = 0 + -182.6666667

Reorder the terms:
182.6666667 + -182.6666667 + -273.3333333x + x2 = 0 + -182.6666667

Combine like terms: 182.6666667 + -182.6666667 = 0.0000000
0.0000000 + -273.3333333x + x2 = 0 + -182.6666667
-273.3333333x + x2 = 0 + -182.6666667

Combine like terms: 0 + -182.6666667 = -182.6666667
-273.3333333x + x2 = -182.6666667

The x term is -273.3333333x.  Take half its coefficient (-136.6666667).
Square it (18677.77779) and add it to both sides.

Add '18677.77779' to each side of the equation.
-273.3333333x + 18677.77779 + x2 = -182.6666667 + 18677.77779

Reorder the terms:
18677.77779 + -273.3333333x + x2 = -182.6666667 + 18677.77779

Combine like terms: -182.6666667 + 18677.77779 = 18495.1111233
18677.77779 + -273.3333333x + x2 = 18495.1111233

Factor a perfect square on the left side:
(x + -136.6666667)(x + -136.6666667) = 18495.1111233

Calculate the square root of the right side: 135.996732032

Break this problem into two subproblems by setting 
(x + -136.6666667) equal to 135.996732032 and -135.996732032.

Subproblem 1

x + -136.6666667 = 135.996732032 Simplifying x + -136.6666667 = 135.996732032 Reorder the terms: -136.6666667 + x = 135.996732032 Solving -136.6666667 + x = 135.996732032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '136.6666667' to each side of the equation. -136.6666667 + 136.6666667 + x = 135.996732032 + 136.6666667 Combine like terms: -136.6666667 + 136.6666667 = 0.0000000 0.0000000 + x = 135.996732032 + 136.6666667 x = 135.996732032 + 136.6666667 Combine like terms: 135.996732032 + 136.6666667 = 272.663398732 x = 272.663398732 Simplifying x = 272.663398732

Subproblem 2

x + -136.6666667 = -135.996732032 Simplifying x + -136.6666667 = -135.996732032 Reorder the terms: -136.6666667 + x = -135.996732032 Solving -136.6666667 + x = -135.996732032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '136.6666667' to each side of the equation. -136.6666667 + 136.6666667 + x = -135.996732032 + 136.6666667 Combine like terms: -136.6666667 + 136.6666667 = 0.0000000 0.0000000 + x = -135.996732032 + 136.6666667 x = -135.996732032 + 136.6666667 Combine like terms: -135.996732032 + 136.6666667 = 0.669934668 x = 0.669934668 Simplifying x = 0.669934668

Solution

The solution to the problem is based on the solutions from the subproblems. x = {272.663398732, 0.669934668}

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