(x+1)*(x+2)=24.75

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Solution for (x+1)*(x+2)=24.75 equation:


Simplifying
(x + 1)(x + 2) = 24.75

Reorder the terms:
(1 + x)(x + 2) = 24.75

Reorder the terms:
(1 + x)(2 + x) = 24.75

Multiply (1 + x) * (2 + x)
(1(2 + x) + x(2 + x)) = 24.75
((2 * 1 + x * 1) + x(2 + x)) = 24.75
((2 + 1x) + x(2 + x)) = 24.75
(2 + 1x + (2 * x + x * x)) = 24.75
(2 + 1x + (2x + x2)) = 24.75

Combine like terms: 1x + 2x = 3x
(2 + 3x + x2) = 24.75

Solving
2 + 3x + x2 = 24.75

Solving for variable 'x'.

Reorder the terms:
2 + -24.75 + 3x + x2 = 24.75 + -24.75

Combine like terms: 2 + -24.75 = -22.75
-22.75 + 3x + x2 = 24.75 + -24.75

Combine like terms: 24.75 + -24.75 = 0.00
-22.75 + 3x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '22.75' to each side of the equation.
-22.75 + 3x + 22.75 + x2 = 0.00 + 22.75

Reorder the terms:
-22.75 + 22.75 + 3x + x2 = 0.00 + 22.75

Combine like terms: -22.75 + 22.75 = 0.00
0.00 + 3x + x2 = 0.00 + 22.75
3x + x2 = 0.00 + 22.75

Combine like terms: 0.00 + 22.75 = 22.75
3x + x2 = 22.75

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 = 22.75 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 22.75 + 2.25

Combine like terms: 22.75 + 2.25 = 25
2.25 + 3x + x2 = 25

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 1.5) equal to 5 and -5.

Subproblem 1

x + 1.5 = 5 Simplifying x + 1.5 = 5 Reorder the terms: 1.5 + x = 5 Solving 1.5 + x = 5 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 = 5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 5 + -1.5 x = 5 + -1.5 Combine like terms: 5 + -1.5 = 3.5 x = 3.5 Simplifying x = 3.5

Subproblem 2

x + 1.5 = -5 Simplifying x + 1.5 = -5 Reorder the terms: 1.5 + x = -5 Solving 1.5 + x = -5 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 = -5 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -5 + -1.5 x = -5 + -1.5 Combine like terms: -5 + -1.5 = -6.5 x = -6.5 Simplifying x = -6.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {3.5, -6.5}

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