2x^2+4x+9=x^2-2x+2

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Solution for 2x^2+4x+9=x^2-2x+2 equation:


Simplifying
2x2 + 4x + 9 = x2 + -2x + 2

Reorder the terms:
9 + 4x + 2x2 = x2 + -2x + 2

Reorder the terms:
9 + 4x + 2x2 = 2 + -2x + x2

Solving
9 + 4x + 2x2 = 2 + -2x + x2

Solving for variable 'x'.

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

Combine like terms: 9 + -2 = 7
7 + 4x + 2x + 2x2 + -1x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Combine like terms: 4x + 2x = 6x
7 + 6x + 2x2 + -1x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
7 + 6x + 1x2 = 2 + -2x + x2 + -2 + 2x + -1x2

Reorder the terms:
7 + 6x + 1x2 = 2 + -2 + -2x + 2x + x2 + -1x2

Combine like terms: 2 + -2 = 0
7 + 6x + 1x2 = 0 + -2x + 2x + x2 + -1x2
7 + 6x + 1x2 = -2x + 2x + x2 + -1x2

Combine like terms: -2x + 2x = 0
7 + 6x + 1x2 = 0 + x2 + -1x2
7 + 6x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
7 + 6x + 1x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-7' to each side of the equation.
7 + 6x + -7 + x2 = 0 + -7

Reorder the terms:
7 + -7 + 6x + x2 = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 6x + x2 = 0 + -7
6x + x2 = 0 + -7

Combine like terms: 0 + -7 = -7
6x + x2 = -7

The x term is 6x.  Take half its coefficient (3).
Square it (9) and add it to both sides.

Add '9' to each side of the equation.
6x + 9 + x2 = -7 + 9

Reorder the terms:
9 + 6x + x2 = -7 + 9

Combine like terms: -7 + 9 = 2
9 + 6x + x2 = 2

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

Calculate the square root of the right side: 1.414213562

Break this problem into two subproblems by setting 
(x + 3) equal to 1.414213562 and -1.414213562.

Subproblem 1

x + 3 = 1.414213562 Simplifying x + 3 = 1.414213562 Reorder the terms: 3 + x = 1.414213562 Solving 3 + x = 1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + x = 1.414213562 + -3 x = 1.414213562 + -3 Combine like terms: 1.414213562 + -3 = -1.585786438 x = -1.585786438 Simplifying x = -1.585786438

Subproblem 2

x + 3 = -1.414213562 Simplifying x + 3 = -1.414213562 Reorder the terms: 3 + x = -1.414213562 Solving 3 + x = -1.414213562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -1.414213562 + -3 Combine like terms: 3 + -3 = 0 0 + x = -1.414213562 + -3 x = -1.414213562 + -3 Combine like terms: -1.414213562 + -3 = -4.414213562 x = -4.414213562 Simplifying x = -4.414213562

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-1.585786438, -4.414213562}

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