(-2x^2+5x-9)-(-x^2-3x-5)+(2x^2-4x+5)=

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Solution for (-2x^2+5x-9)-(-x^2-3x-5)+(2x^2-4x+5)= equation:


Simplifying
(-2x2 + 5x + -9) + -1(-1x2 + -3x + -5) + (2x2 + -4x + 5) = 0

Reorder the terms:
(-9 + 5x + -2x2) + -1(-1x2 + -3x + -5) + (2x2 + -4x + 5) = 0

Remove parenthesis around (-9 + 5x + -2x2)
-9 + 5x + -2x2 + -1(-1x2 + -3x + -5) + (2x2 + -4x + 5) = 0

Reorder the terms:
-9 + 5x + -2x2 + -1(-5 + -3x + -1x2) + (2x2 + -4x + 5) = 0
-9 + 5x + -2x2 + (-5 * -1 + -3x * -1 + -1x2 * -1) + (2x2 + -4x + 5) = 0
-9 + 5x + -2x2 + (5 + 3x + 1x2) + (2x2 + -4x + 5) = 0

Reorder the terms:
-9 + 5x + -2x2 + 5 + 3x + 1x2 + (5 + -4x + 2x2) = 0

Remove parenthesis around (5 + -4x + 2x2)
-9 + 5x + -2x2 + 5 + 3x + 1x2 + 5 + -4x + 2x2 = 0

Reorder the terms:
-9 + 5 + 5 + 5x + 3x + -4x + -2x2 + 1x2 + 2x2 = 0

Combine like terms: -9 + 5 = -4
-4 + 5 + 5x + 3x + -4x + -2x2 + 1x2 + 2x2 = 0

Combine like terms: -4 + 5 = 1
1 + 5x + 3x + -4x + -2x2 + 1x2 + 2x2 = 0

Combine like terms: 5x + 3x = 8x
1 + 8x + -4x + -2x2 + 1x2 + 2x2 = 0

Combine like terms: 8x + -4x = 4x
1 + 4x + -2x2 + 1x2 + 2x2 = 0

Combine like terms: -2x2 + 1x2 = -1x2
1 + 4x + -1x2 + 2x2 = 0

Combine like terms: -1x2 + 2x2 = 1x2
1 + 4x + 1x2 = 0

Solving
1 + 4x + 1x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 4x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 4x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x + x2 = 0 + -1
4x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
4x + x2 = -1

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = -1 + 4

Reorder the terms:
4 + 4x + x2 = -1 + 4

Combine like terms: -1 + 4 = 3
4 + 4x + x2 = 3

Factor a perfect square on the left side:
(x + 2)(x + 2) = 3

Calculate the square root of the right side: 1.732050808

Break this problem into two subproblems by setting 
(x + 2) equal to 1.732050808 and -1.732050808.

Subproblem 1

x + 2 = 1.732050808 Simplifying x + 2 = 1.732050808 Reorder the terms: 2 + x = 1.732050808 Solving 2 + x = 1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = 1.732050808 + -2 x = 1.732050808 + -2 Combine like terms: 1.732050808 + -2 = -0.267949192 x = -0.267949192 Simplifying x = -0.267949192

Subproblem 2

x + 2 = -1.732050808 Simplifying x + 2 = -1.732050808 Reorder the terms: 2 + x = -1.732050808 Solving 2 + x = -1.732050808 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -1.732050808 + -2 Combine like terms: 2 + -2 = 0 0 + x = -1.732050808 + -2 x = -1.732050808 + -2 Combine like terms: -1.732050808 + -2 = -3.732050808 x = -3.732050808 Simplifying x = -3.732050808

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.267949192, -3.732050808}

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