x^2+5x-1-2x^2-2x+5-3x^2+4=

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Solution for x^2+5x-1-2x^2-2x+5-3x^2+4= equation:


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

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

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

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

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

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

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

Solving
8 + 3x + -4x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-2 + -0.75x + x2 = 0

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -0.75x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -0.75x + x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -0.75x + x2 = 0 + 2
-0.75x + x2 = 0 + 2

Combine like terms: 0 + 2 = 2
-0.75x + x2 = 2

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 + 0.140625

Reorder the terms:
0.140625 + -0.75x + x2 = 2 + 0.140625

Combine like terms: 2 + 0.140625 = 2.140625
0.140625 + -0.75x + x2 = 2.140625

Factor a perfect square on the left side:
(x + -0.375)(x + -0.375) = 2.140625

Calculate the square root of the right side: 1.463087489

Break this problem into two subproblems by setting 
(x + -0.375) equal to 1.463087489 and -1.463087489.

Subproblem 1

x + -0.375 = 1.463087489 Simplifying x + -0.375 = 1.463087489 Reorder the terms: -0.375 + x = 1.463087489 Solving -0.375 + x = 1.463087489 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 = 1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = 1.463087489 + 0.375 x = 1.463087489 + 0.375 Combine like terms: 1.463087489 + 0.375 = 1.838087489 x = 1.838087489 Simplifying x = 1.838087489

Subproblem 2

x + -0.375 = -1.463087489 Simplifying x + -0.375 = -1.463087489 Reorder the terms: -0.375 + x = -1.463087489 Solving -0.375 + x = -1.463087489 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 = -1.463087489 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + x = -1.463087489 + 0.375 x = -1.463087489 + 0.375 Combine like terms: -1.463087489 + 0.375 = -1.088087489 x = -1.088087489 Simplifying x = -1.088087489

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.838087489, -1.088087489}

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