2x^2+7x-2=-2x^2+2x

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Solution for 2x^2+7x-2=-2x^2+2x equation:


Simplifying
2x2 + 7x + -2 = -2x2 + 2x

Reorder the terms:
-2 + 7x + 2x2 = -2x2 + 2x

Reorder the terms:
-2 + 7x + 2x2 = 2x + -2x2

Solving
-2 + 7x + 2x2 = 2x + -2x2

Solving for variable 'x'.

Reorder the terms:
-2 + 7x + -2x + 2x2 + 2x2 = 2x + -2x2 + -2x + 2x2

Combine like terms: 7x + -2x = 5x
-2 + 5x + 2x2 + 2x2 = 2x + -2x2 + -2x + 2x2

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

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

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

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

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

Divide each side by '4'.
-0.5 + 1.25x + x2 = 0

Move the constant term to the right:

Add '0.5' to each side of the equation.
-0.5 + 1.25x + 0.5 + x2 = 0 + 0.5

Reorder the terms:
-0.5 + 0.5 + 1.25x + x2 = 0 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + 1.25x + x2 = 0 + 0.5
1.25x + x2 = 0 + 0.5

Combine like terms: 0 + 0.5 = 0.5
1.25x + x2 = 0.5

The x term is 1.25x.  Take half its coefficient (0.625).
Square it (0.390625) and add it to both sides.

Add '0.390625' to each side of the equation.
1.25x + 0.390625 + x2 = 0.5 + 0.390625

Reorder the terms:
0.390625 + 1.25x + x2 = 0.5 + 0.390625

Combine like terms: 0.5 + 0.390625 = 0.890625
0.390625 + 1.25x + x2 = 0.890625

Factor a perfect square on the left side:
(x + 0.625)(x + 0.625) = 0.890625

Calculate the square root of the right side: 0.943729304

Break this problem into two subproblems by setting 
(x + 0.625) equal to 0.943729304 and -0.943729304.

Subproblem 1

x + 0.625 = 0.943729304 Simplifying x + 0.625 = 0.943729304 Reorder the terms: 0.625 + x = 0.943729304 Solving 0.625 + x = 0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = 0.943729304 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = 0.943729304 + -0.625 x = 0.943729304 + -0.625 Combine like terms: 0.943729304 + -0.625 = 0.318729304 x = 0.318729304 Simplifying x = 0.318729304

Subproblem 2

x + 0.625 = -0.943729304 Simplifying x + 0.625 = -0.943729304 Reorder the terms: 0.625 + x = -0.943729304 Solving 0.625 + x = -0.943729304 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.625' to each side of the equation. 0.625 + -0.625 + x = -0.943729304 + -0.625 Combine like terms: 0.625 + -0.625 = 0.000 0.000 + x = -0.943729304 + -0.625 x = -0.943729304 + -0.625 Combine like terms: -0.943729304 + -0.625 = -1.568729304 x = -1.568729304 Simplifying x = -1.568729304

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.318729304, -1.568729304}

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