(4x+1)(x+2)=-2

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Solution for (4x+1)(x+2)=-2 equation:


Simplifying
(4x + 1)(x + 2) = -2

Reorder the terms:
(1 + 4x)(x + 2) = -2

Reorder the terms:
(1 + 4x)(2 + x) = -2

Multiply (1 + 4x) * (2 + x)
(1(2 + x) + 4x * (2 + x)) = -2
((2 * 1 + x * 1) + 4x * (2 + x)) = -2
((2 + 1x) + 4x * (2 + x)) = -2
(2 + 1x + (2 * 4x + x * 4x)) = -2
(2 + 1x + (8x + 4x2)) = -2

Combine like terms: 1x + 8x = 9x
(2 + 9x + 4x2) = -2

Solving
2 + 9x + 4x2 = -2

Solving for variable 'x'.

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

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

Combine like terms: -2 + 2 = 0
4 + 9x + 4x2 = 0

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

Divide each side by '4'.
1 + 2.25x + x2 = 0

Move the constant term to the right:

Add '-1' to each side of the equation.
1 + 2.25x + -1 + x2 = 0 + -1

Reorder the terms:
1 + -1 + 2.25x + x2 = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 2.25x + x2 = 0 + -1
2.25x + x2 = 0 + -1

Combine like terms: 0 + -1 = -1
2.25x + x2 = -1

The x term is 2.25x.  Take half its coefficient (1.125).
Square it (1.265625) and add it to both sides.

Add '1.265625' to each side of the equation.
2.25x + 1.265625 + x2 = -1 + 1.265625

Reorder the terms:
1.265625 + 2.25x + x2 = -1 + 1.265625

Combine like terms: -1 + 1.265625 = 0.265625
1.265625 + 2.25x + x2 = 0.265625

Factor a perfect square on the left side:
(x + 1.125)(x + 1.125) = 0.265625

Calculate the square root of the right side: 0.515388203

Break this problem into two subproblems by setting 
(x + 1.125) equal to 0.515388203 and -0.515388203.

Subproblem 1

x + 1.125 = 0.515388203 Simplifying x + 1.125 = 0.515388203 Reorder the terms: 1.125 + x = 0.515388203 Solving 1.125 + x = 0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = 0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 0.515388203 + -1.125 x = 0.515388203 + -1.125 Combine like terms: 0.515388203 + -1.125 = -0.609611797 x = -0.609611797 Simplifying x = -0.609611797

Subproblem 2

x + 1.125 = -0.515388203 Simplifying x + 1.125 = -0.515388203 Reorder the terms: 1.125 + x = -0.515388203 Solving 1.125 + x = -0.515388203 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.125' to each side of the equation. 1.125 + -1.125 + x = -0.515388203 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -0.515388203 + -1.125 x = -0.515388203 + -1.125 Combine like terms: -0.515388203 + -1.125 = -1.640388203 x = -1.640388203 Simplifying x = -1.640388203

Solution

The solution to the problem is based on the solutions from the subproblems. x = {-0.609611797, -1.640388203}

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