(x+2)*(x+3)=100

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Solution for (x+2)*(x+3)=100 equation:


Simplifying
(x + 2)(x + 3) = 100

Reorder the terms:
(2 + x)(x + 3) = 100

Reorder the terms:
(2 + x)(3 + x) = 100

Multiply (2 + x) * (3 + x)
(2(3 + x) + x(3 + x)) = 100
((3 * 2 + x * 2) + x(3 + x)) = 100
((6 + 2x) + x(3 + x)) = 100
(6 + 2x + (3 * x + x * x)) = 100
(6 + 2x + (3x + x2)) = 100

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 100

Solving
6 + 5x + x2 = 100

Solving for variable 'x'.

Reorder the terms:
6 + -100 + 5x + x2 = 100 + -100

Combine like terms: 6 + -100 = -94
-94 + 5x + x2 = 100 + -100

Combine like terms: 100 + -100 = 0
-94 + 5x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '94' to each side of the equation.
-94 + 5x + 94 + x2 = 0 + 94

Reorder the terms:
-94 + 94 + 5x + x2 = 0 + 94

Combine like terms: -94 + 94 = 0
0 + 5x + x2 = 0 + 94
5x + x2 = 0 + 94

Combine like terms: 0 + 94 = 94
5x + x2 = 94

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 = 94 + 6.25

Reorder the terms:
6.25 + 5x + x2 = 94 + 6.25

Combine like terms: 94 + 6.25 = 100.25
6.25 + 5x + x2 = 100.25

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 100.25

Calculate the square root of the right side: 10.012492197

Break this problem into two subproblems by setting 
(x + 2.5) equal to 10.012492197 and -10.012492197.

Subproblem 1

x + 2.5 = 10.012492197 Simplifying x + 2.5 = 10.012492197 Reorder the terms: 2.5 + x = 10.012492197 Solving 2.5 + x = 10.012492197 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 = 10.012492197 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 10.012492197 + -2.5 x = 10.012492197 + -2.5 Combine like terms: 10.012492197 + -2.5 = 7.512492197 x = 7.512492197 Simplifying x = 7.512492197

Subproblem 2

x + 2.5 = -10.012492197 Simplifying x + 2.5 = -10.012492197 Reorder the terms: 2.5 + x = -10.012492197 Solving 2.5 + x = -10.012492197 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 = -10.012492197 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -10.012492197 + -2.5 x = -10.012492197 + -2.5 Combine like terms: -10.012492197 + -2.5 = -12.512492197 x = -12.512492197 Simplifying x = -12.512492197

Solution

The solution to the problem is based on the solutions from the subproblems. x = {7.512492197, -12.512492197}

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