-2x^2-4x+7=0

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Solution for -2x^2-4x+7=0 equation:


Simplifying
-2x2 + -4x + 7 = 0

Reorder the terms:
7 + -4x + -2x2 = 0

Solving
7 + -4x + -2x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
-3.5 + 2x + x2 = 0

Move the constant term to the right:

Add '3.5' to each side of the equation.
-3.5 + 2x + 3.5 + x2 = 0 + 3.5

Reorder the terms:
-3.5 + 3.5 + 2x + x2 = 0 + 3.5

Combine like terms: -3.5 + 3.5 = 0.0
0.0 + 2x + x2 = 0 + 3.5
2x + x2 = 0 + 3.5

Combine like terms: 0 + 3.5 = 3.5
2x + x2 = 3.5

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 3.5 + 1

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

Combine like terms: 3.5 + 1 = 4.5
1 + 2x + x2 = 4.5

Factor a perfect square on the left side:
(x + 1)(x + 1) = 4.5

Calculate the square root of the right side: 2.121320344

Break this problem into two subproblems by setting 
(x + 1) equal to 2.121320344 and -2.121320344.

Subproblem 1

x + 1 = 2.121320344 Simplifying x + 1 = 2.121320344 Reorder the terms: 1 + x = 2.121320344 Solving 1 + x = 2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 2.121320344 + -1 Combine like terms: 1 + -1 = 0 0 + x = 2.121320344 + -1 x = 2.121320344 + -1 Combine like terms: 2.121320344 + -1 = 1.121320344 x = 1.121320344 Simplifying x = 1.121320344

Subproblem 2

x + 1 = -2.121320344 Simplifying x + 1 = -2.121320344 Reorder the terms: 1 + x = -2.121320344 Solving 1 + x = -2.121320344 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -2.121320344 + -1 Combine like terms: 1 + -1 = 0 0 + x = -2.121320344 + -1 x = -2.121320344 + -1 Combine like terms: -2.121320344 + -1 = -3.121320344 x = -3.121320344 Simplifying x = -3.121320344

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.121320344, -3.121320344}

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