x^2+3x-1.05=0

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Solution for x^2+3x-1.05=0 equation:


Simplifying
x2 + 3x + -1.05 = 0

Reorder the terms:
-1.05 + 3x + x2 = 0

Solving
-1.05 + 3x + x2 = 0

Solving for variable 'x'.

Begin completing the square.

Move the constant term to the right:

Add '1.05' to each side of the equation.
-1.05 + 3x + 1.05 + x2 = 0 + 1.05

Reorder the terms:
-1.05 + 1.05 + 3x + x2 = 0 + 1.05

Combine like terms: -1.05 + 1.05 = 0.00
0.00 + 3x + x2 = 0 + 1.05
3x + x2 = 0 + 1.05

Combine like terms: 0 + 1.05 = 1.05
3x + x2 = 1.05

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 = 1.05 + 2.25

Reorder the terms:
2.25 + 3x + x2 = 1.05 + 2.25

Combine like terms: 1.05 + 2.25 = 3.3
2.25 + 3x + x2 = 3.3

Factor a perfect square on the left side:
(x + 1.5)(x + 1.5) = 3.3

Calculate the square root of the right side: 1.816590212

Break this problem into two subproblems by setting 
(x + 1.5) equal to 1.816590212 and -1.816590212.

Subproblem 1

x + 1.5 = 1.816590212 Simplifying x + 1.5 = 1.816590212 Reorder the terms: 1.5 + x = 1.816590212 Solving 1.5 + x = 1.816590212 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 = 1.816590212 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 1.816590212 + -1.5 x = 1.816590212 + -1.5 Combine like terms: 1.816590212 + -1.5 = 0.316590212 x = 0.316590212 Simplifying x = 0.316590212

Subproblem 2

x + 1.5 = -1.816590212 Simplifying x + 1.5 = -1.816590212 Reorder the terms: 1.5 + x = -1.816590212 Solving 1.5 + x = -1.816590212 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 = -1.816590212 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -1.816590212 + -1.5 x = -1.816590212 + -1.5 Combine like terms: -1.816590212 + -1.5 = -3.316590212 x = -3.316590212 Simplifying x = -3.316590212

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.316590212, -3.316590212}

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