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

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


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

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

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

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

Combine like terms: 2x + 1x = 3x
(2 + 3x + x2) = 4

Solving
2 + 3x + x2 = 4

Solving for variable 'x'.

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + 3x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + 3x + x2 = 0 + 2

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

Combine like terms: 0 + 2 = 2
3x + x2 = 2

The x term is 3x.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3x + 2.25 + x2 = 2 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 2 + 2.25

Combine like terms: 2 + 2.25 = 4.25
2.25 + 3x + x2 = 4.25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 4.25

Calculate the square root of the right side: 2.061552813

Break this problem into two subproblems by setting 
(x + 1.5) equal to 2.061552813 and -2.061552813.

Subproblem 1

x + 1.5 = 2.061552813 Simplifying x + 1.5 = 2.061552813 Reorder the terms: 1.5 + x = 2.061552813 Solving 1.5 + x = 2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 2.061552813 + -1.5 x = 2.061552813 + -1.5 Combine like terms: 2.061552813 + -1.5 = 0.561552813 x = 0.561552813 Simplifying x = 0.561552813

Subproblem 2

x + 1.5 = -2.061552813 Simplifying x + 1.5 = -2.061552813 Reorder the terms: 1.5 + x = -2.061552813 Solving 1.5 + x = -2.061552813 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -2.061552813 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -2.061552813 + -1.5 x = -2.061552813 + -1.5 Combine like terms: -2.061552813 + -1.5 = -3.561552813 x = -3.561552813 Simplifying x = -3.561552813

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.561552813, -3.561552813}

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