(x+2)(x+3)=24.75

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Solution for (x+2)(x+3)=24.75 equation:


Simplifying
(x + 2)(x + 3) = 24.75

Reorder the terms:
(2 + x)(x + 3) = 24.75

Reorder the terms:
(2 + x)(3 + x) = 24.75

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 24.75
((3 * 2 + x * 2) + x(3 + x)) = 24.75
((6 + 2x) + x(3 + x)) = 24.75
(6 + 2x + (3 * x + x * x)) = 24.75
(6 + 2x + (3x + x2)) = 24.75

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 24.75

Solving
6 + 5x + x2 = 24.75

Solving for variable 'x'.

Reorder the terms:
6 + -24.75 + 5x + x2 = 24.75 + -24.75

Combine like terms: 6 + -24.75 = -18.75
-18.75 + 5x + x2 = 24.75 + -24.75

Combine like terms: 24.75 + -24.75 = 0.00
-18.75 + 5x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '18.75' to each side of the equation.
-18.75 + 5x + 18.75 + x2 = 0.00 + 18.75

Reorder the terms:
-18.75 + 18.75 + 5x + x2 = 0.00 + 18.75

Combine like terms: -18.75 + 18.75 = 0.00
0.00 + 5x + x2 = 0.00 + 18.75
5x + x2 = 0.00 + 18.75

Combine like terms: 0.00 + 18.75 = 18.75
5x + x2 = 18.75

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = 18.75 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 18.75 + 6.25

Combine like terms: 18.75 + 6.25 = 25
6.25 + 5x + x2 = 25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 25

Calculate the square root of the right side: 5

Break this problem into two subproblems by setting 
(x + 2.5) equal to 5 and -5.

Subproblem 1

x + 2.5 = 5 Simplifying x + 2.5 = 5 Reorder the terms: 2.5 + x = 5 Solving 2.5 + x = 5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 5 + -2.5 x = 5 + -2.5 Combine like terms: 5 + -2.5 = 2.5 x = 2.5 Simplifying x = 2.5

Subproblem 2

x + 2.5 = -5 Simplifying x + 2.5 = -5 Reorder the terms: 2.5 + x = -5 Solving 2.5 + x = -5 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -5 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -5 + -2.5 x = -5 + -2.5 Combine like terms: -5 + -2.5 = -7.5 x = -7.5 Simplifying x = -7.5

Solution

The solution to the problem is based on the solutions from the subproblems. x = {2.5, -7.5}

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