1-x=-x(2+x)+1.75(2+x)

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Solution for 1-x=-x(2+x)+1.75(2+x) equation:


Simplifying
1 + -1x = -1x(2 + x) + 1.75(2 + x)
1 + -1x = (2 * -1x + x * -1x) + 1.75(2 + x)
1 + -1x = (-2x + -1x2) + 1.75(2 + x)
1 + -1x = -2x + -1x2 + (2 * 1.75 + x * 1.75)
1 + -1x = -2x + -1x2 + (3.5 + 1.75x)

Reorder the terms:
1 + -1x = 3.5 + -2x + 1.75x + -1x2

Combine like terms: -2x + 1.75x = -0.25x
1 + -1x = 3.5 + -0.25x + -1x2

Solving
1 + -1x = 3.5 + -0.25x + -1x2

Solving for variable 'x'.

Reorder the terms:
1 + -3.5 + -1x + 0.25x + x2 = 3.5 + -0.25x + -1x2 + -3.5 + 0.25x + x2

Combine like terms: 1 + -3.5 = -2.5
-2.5 + -1x + 0.25x + x2 = 3.5 + -0.25x + -1x2 + -3.5 + 0.25x + x2

Combine like terms: -1x + 0.25x = -0.75x
-2.5 + -0.75x + x2 = 3.5 + -0.25x + -1x2 + -3.5 + 0.25x + x2

Reorder the terms:
-2.5 + -0.75x + x2 = 3.5 + -3.5 + -0.25x + 0.25x + -1x2 + x2

Combine like terms: 3.5 + -3.5 = 0.0
-2.5 + -0.75x + x2 = 0.0 + -0.25x + 0.25x + -1x2 + x2
-2.5 + -0.75x + x2 = -0.25x + 0.25x + -1x2 + x2

Combine like terms: -0.25x + 0.25x = 0.00
-2.5 + -0.75x + x2 = 0.00 + -1x2 + x2
-2.5 + -0.75x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2.5 + -0.75x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2.5' to each side of the equation.
-2.5 + -0.75x + 2.5 + x2 = 0 + 2.5

Reorder the terms:
-2.5 + 2.5 + -0.75x + x2 = 0 + 2.5

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + -0.75x + x2 = 0 + 2.5
-0.75x + x2 = 0 + 2.5

Combine like terms: 0 + 2.5 = 2.5
-0.75x + x2 = 2.5

The x term is -0.75x.  Take half its coefficient (-0.375).
Square it (0.140625) and add it to both sides.

Add '0.140625' to each side of the equation.
-0.75x + 0.140625 + x2 = 2.5 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 2.5 + 0.140625

Combine like terms: 2.5 + 0.140625 = 2.640625
0.140625 + -0.75x + x2 = 2.640625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 2.640625

Calculate the square root of the right side: 1.625

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.625 and -1.625.

Subproblem 1

x + -0.375 = 1.625 Simplifying x + -0.375 = 1.625 Reorder the terms: -0.375 + x = 1.625 Solving -0.375 + x = 1.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = 1.625 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.625 + 0.375 x = 1.625 + 0.375 Combine like terms: 1.625 + 0.375 = 2 x = 2 Simplifying x = 2

Subproblem 2

x + -0.375 = -1.625 Simplifying x + -0.375 = -1.625 Reorder the terms: -0.375 + x = -1.625 Solving -0.375 + x = -1.625 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + x = -1.625 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.625 + 0.375 x = -1.625 + 0.375 Combine like terms: -1.625 + 0.375 = -1.25 x = -1.25 Simplifying x = -1.25

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2, -1.25}

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