x+(x+3)(x-45)=

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Solution for x+(x+3)(x-45)= equation: 


Simplifying
x + (x + 3)(x + -45) = 0

Reorder the terms:
x + (3 + x)(x + -45) = 0

Reorder the terms:
x + (3 + x)(-45 + x) = 0

Multiply (3 + x) * (-45 + x)
x + (3(-45 + x) + x(-45 + x)) = 0
x + ((-45 * 3 + x * 3) + x(-45 + x)) = 0
x + ((-135 + 3x) + x(-45 + x)) = 0
x + (-135 + 3x + (-45 * x + x * x)) = 0
x + (-135 + 3x + (-45x + x2)) = 0

Combine like terms: 3x + -45x = -42x
x + (-135 + -42x + x2) = 0

Reorder the terms:
-135 + x + -42x + x2 = 0

Combine like terms: x + -42x = -41x
-135 + -41x + x2 = 0

Solving
-135 + -41x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '135' to each side of the equation.
-135 + -41x + 135 + x2 = 0 + 135

Reorder the terms:
-135 + 135 + -41x + x2 = 0 + 135

Combine like terms: -135 + 135 = 0
0 + -41x + x2 = 0 + 135
-41x + x2 = 0 + 135

Combine like terms: 0 + 135 = 135
-41x + x2 = 135

The x term is -41x.  Take half its coefficient (-20.5).
Square it (420.25) and add it to both sides.

Add '420.25' to each side of the equation.
-41x + 420.25 + x2 = 135 + 420.25

Reorder the terms:
420.25 + -41x + x2 = 135 + 420.25

Combine like terms: 135 + 420.25 = 555.25
420.25 + -41x + x2 = 555.25

Factor a perfect square on the left side:
(x + -20.5)(x + -20.5) = 555.25

Calculate the square root of the right side: 23.563743336

Break this problem into two subproblems by setting 
(x + -20.5) equal to 23.563743336 and -23.563743336.


Subproblem 1
x + -20.5 = 23.563743336

Simplifying
x + -20.5 = 23.563743336

Reorder the terms:
-20.5 + x = 23.563743336

Solving
-20.5 + x = 23.563743336

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20.5' to each side of the equation.
-20.5 + 20.5 + x = 23.563743336 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + x = 23.563743336 + 20.5
x = 23.563743336 + 20.5

Combine like terms: 23.563743336 + 20.5 = 44.063743336
x = 44.063743336

Simplifying
x = 44.063743336


Subproblem 2
x + -20.5 = -23.563743336

Simplifying
x + -20.5 = -23.563743336

Reorder the terms:
-20.5 + x = -23.563743336

Solving
-20.5 + x = -23.563743336

Solving for variable 'x'.

Move all terms containing x to the left, all other terms to the right.

Add '20.5' to each side of the equation.
-20.5 + 20.5 + x = -23.563743336 + 20.5

Combine like terms: -20.5 + 20.5 = 0.0
0.0 + x = -23.563743336 + 20.5
x = -23.563743336 + 20.5

Combine like terms: -23.563743336 + 20.5 = -3.063743336
x = -3.063743336

Simplifying
x = -3.063743336


Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {44.063743336, -3.063743336}

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