x^2+x+1=(2x-1)(x+3)

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Solution for x^2+x+1=(2x-1)(x+3) equation:


Simplifying
x2 + x + 1 = (2x + -1)(x + 3)

Reorder the terms:
1 + x + x2 = (2x + -1)(x + 3)

Reorder the terms:
1 + x + x2 = (-1 + 2x)(x + 3)

Reorder the terms:
1 + x + x2 = (-1 + 2x)(3 + x)

Multiply (-1 + 2x) * (3 + x)
1 + x + x2 = (-1(3 + x) + 2x * (3 + x))
1 + x + x2 = ((3 * -1 + x * -1) + 2x * (3 + x))
1 + x + x2 = ((-3 + -1x) + 2x * (3 + x))
1 + x + x2 = (-3 + -1x + (3 * 2x + x * 2x))
1 + x + x2 = (-3 + -1x + (6x + 2x2))

Combine like terms: -1x + 6x = 5x
1 + x + x2 = (-3 + 5x + 2x2)

Solving
1 + x + x2 = -3 + 5x + 2x2

Solving for variable 'x'.

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

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

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

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

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

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

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

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

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-4 + 4x + x2 = 0

Move the constant term to the right:

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

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

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

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

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 = 4 + 4

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

Combine like terms: 4 + 4 = 8
4 + 4x + x2 = 8

Factor a perfect square on the left side:
(x + 2)(x + 2) = 8

Calculate the square root of the right side: 2.828427125

Break this problem into two subproblems by setting 
(x + 2) equal to 2.828427125 and -2.828427125.

Subproblem 1

x + 2 = 2.828427125 Simplifying x + 2 = 2.828427125 Reorder the terms: 2 + x = 2.828427125 Solving 2 + x = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.828427125 + -2 x = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 x = 0.828427125 Simplifying x = 0.828427125

Subproblem 2

x + 2 = -2.828427125 Simplifying x + 2 = -2.828427125 Reorder the terms: 2 + x = -2.828427125 Solving 2 + x = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.828427125 + -2 x = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 x = -4.828427125 Simplifying x = -4.828427125

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.828427125, -4.828427125}

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