0.5x(x-35)+x(-x-46)=360

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Solution for 0.5x(x-35)+x(-x-46)=360 equation:


Simplifying
0.5x(x + -35) + x(-1x + -46) = 360

Reorder the terms:
0.5x(-35 + x) + x(-1x + -46) = 360
(-35 * 0.5x + x * 0.5x) + x(-1x + -46) = 360
(-17.5x + 0.5x2) + x(-1x + -46) = 360

Reorder the terms:
-17.5x + 0.5x2 + x(-46 + -1x) = 360
-17.5x + 0.5x2 + (-46 * x + -1x * x) = 360
-17.5x + 0.5x2 + (-46x + -1x2) = 360

Reorder the terms:
-17.5x + -46x + 0.5x2 + -1x2 = 360

Combine like terms: -17.5x + -46x = -63.5x
-63.5x + 0.5x2 + -1x2 = 360

Combine like terms: 0.5x2 + -1x2 = -0.5x2
-63.5x + -0.5x2 = 360

Solving
-63.5x + -0.5x2 = 360

Solving for variable 'x'.

Reorder the terms:
-360 + -63.5x + -0.5x2 = 360 + -360

Combine like terms: 360 + -360 = 0
-360 + -63.5x + -0.5x2 = 0

Begin completing the square.  Divide all terms by
-0.5 the coefficient of the squared term: 

Divide each side by '-0.5'.
720 + 127x + x2 = 0

Move the constant term to the right:

Add '-720' to each side of the equation.
720 + 127x + -720 + x2 = 0 + -720

Reorder the terms:
720 + -720 + 127x + x2 = 0 + -720

Combine like terms: 720 + -720 = 0
0 + 127x + x2 = 0 + -720
127x + x2 = 0 + -720

Combine like terms: 0 + -720 = -720
127x + x2 = -720

The x term is 127x.  Take half its coefficient (63.5).
Square it (4032.25) and add it to both sides.

Add '4032.25' to each side of the equation.
127x + 4032.25 + x2 = -720 + 4032.25

Reorder the terms:
4032.25 + 127x + x2 = -720 + 4032.25

Combine like terms: -720 + 4032.25 = 3312.25
4032.25 + 127x + x2 = 3312.25

Factor a perfect square on the left side:
(x + 63.5)(x + 63.5) = 3312.25

Calculate the square root of the right side: 57.552150264

Break this problem into two subproblems by setting 
(x + 63.5) equal to 57.552150264 and -57.552150264.

Subproblem 1

x + 63.5 = 57.552150264 Simplifying x + 63.5 = 57.552150264 Reorder the terms: 63.5 + x = 57.552150264 Solving 63.5 + x = 57.552150264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-63.5' to each side of the equation. 63.5 + -63.5 + x = 57.552150264 + -63.5 Combine like terms: 63.5 + -63.5 = 0.0 0.0 + x = 57.552150264 + -63.5 x = 57.552150264 + -63.5 Combine like terms: 57.552150264 + -63.5 = -5.947849736 x = -5.947849736 Simplifying x = -5.947849736

Subproblem 2

x + 63.5 = -57.552150264 Simplifying x + 63.5 = -57.552150264 Reorder the terms: 63.5 + x = -57.552150264 Solving 63.5 + x = -57.552150264 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-63.5' to each side of the equation. 63.5 + -63.5 + x = -57.552150264 + -63.5 Combine like terms: 63.5 + -63.5 = 0.0 0.0 + x = -57.552150264 + -63.5 x = -57.552150264 + -63.5 Combine like terms: -57.552150264 + -63.5 = -121.052150264 x = -121.052150264 Simplifying x = -121.052150264

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-5.947849736, -121.052150264}

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