x^2-3x-105=0

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Solution for x^2-3x-105=0 equation:


Simplifying
x2 + -3x + -105 = 0

Reorder the terms:
-105 + -3x + x2 = 0

Solving
-105 + -3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '105' to each side of the equation.
-105 + -3x + 105 + x2 = 0 + 105

Reorder the terms:
-105 + 105 + -3x + x2 = 0 + 105

Combine like terms: -105 + 105 = 0
0 + -3x + x2 = 0 + 105
-3x + x2 = 0 + 105

Combine like terms: 0 + 105 = 105
-3x + x2 = 105

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 = 105 + 2.25

Reorder the terms:
2.25 + -3x + x2 = 105 + 2.25

Combine like terms: 105 + 2.25 = 107.25
2.25 + -3x + x2 = 107.25

Factor a perfect square on the left side:
(x + -1.5)(x + -1.5) = 107.25

Calculate the square root of the right side: 10.356157589

Break this problem into two subproblems by setting 
(x + -1.5) equal to 10.356157589 and -10.356157589.

Subproblem 1

x + -1.5 = 10.356157589 Simplifying x + -1.5 = 10.356157589 Reorder the terms: -1.5 + x = 10.356157589 Solving -1.5 + x = 10.356157589 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 = 10.356157589 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 10.356157589 + 1.5 x = 10.356157589 + 1.5 Combine like terms: 10.356157589 + 1.5 = 11.856157589 x = 11.856157589 Simplifying x = 11.856157589

Subproblem 2

x + -1.5 = -10.356157589 Simplifying x + -1.5 = -10.356157589 Reorder the terms: -1.5 + x = -10.356157589 Solving -1.5 + x = -10.356157589 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 = -10.356157589 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -10.356157589 + 1.5 x = -10.356157589 + 1.5 Combine like terms: -10.356157589 + 1.5 = -8.856157589 x = -8.856157589 Simplifying x = -8.856157589

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.856157589, -8.856157589}

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