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

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


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

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

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

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

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

Solving
-2 + 1x + x2 = 3

Solving for variable 'x'.

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

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

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

Begin completing the square.

Move the constant term to the right:

Add '5' to each side of the equation.
-5 + 1x + 5 + x2 = 0 + 5

Reorder the terms:
-5 + 5 + 1x + x2 = 0 + 5

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

Combine like terms: 0 + 5 = 5
1x + x2 = 5

The x term is 1x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + x + x2 = 5.25

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 5.25

Calculate the square root of the right side: 2.291287847

Break this problem into two subproblems by setting 
(x + 0.5) equal to 2.291287847 and -2.291287847.

Subproblem 1

x + 0.5 = 2.291287847 Simplifying x + 0.5 = 2.291287847 Reorder the terms: 0.5 + x = 2.291287847 Solving 0.5 + x = 2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 2.291287847 + -0.5 x = 2.291287847 + -0.5 Combine like terms: 2.291287847 + -0.5 = 1.791287847 x = 1.791287847 Simplifying x = 1.791287847

Subproblem 2

x + 0.5 = -2.291287847 Simplifying x + 0.5 = -2.291287847 Reorder the terms: 0.5 + x = -2.291287847 Solving 0.5 + x = -2.291287847 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -2.291287847 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -2.291287847 + -0.5 x = -2.291287847 + -0.5 Combine like terms: -2.291287847 + -0.5 = -2.791287847 x = -2.791287847 Simplifying x = -2.791287847

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.791287847, -2.791287847}

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