(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.
-1x + 0.25 + x2 = 5 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 5 + 0.25

Combine like terms: 5 + 0.25 = 5.25
0.25 + -1x + 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 = 2.791287847 x = 2.791287847 Simplifying x = 2.791287847

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 = -1.791287847 x = -1.791287847 Simplifying x = -1.791287847

Solution

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

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