2.3x^2-3.5x-1.2=0

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Solution for 2.3x^2-3.5x-1.2=0 equation:


Simplifying
2.3x2 + -3.5x + -1.2 = 0

Reorder the terms:
-1.2 + -3.5x + 2.3x2 = 0

Solving
-1.2 + -3.5x + 2.3x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
2.3 the coefficient of the squared term: 

Divide each side by '2.3'.
-0.5217391304 + -1.52173913x + x2 = 0

Move the constant term to the right:

Add '0.5217391304' to each side of the equation.
-0.5217391304 + -1.52173913x + 0.5217391304 + x2 = 0 + 0.5217391304

Reorder the terms:
-0.5217391304 + 0.5217391304 + -1.52173913x + x2 = 0 + 0.5217391304

Combine like terms: -0.5217391304 + 0.5217391304 = 0.0000000000
0.0000000000 + -1.52173913x + x2 = 0 + 0.5217391304
-1.52173913x + x2 = 0 + 0.5217391304

Combine like terms: 0 + 0.5217391304 = 0.5217391304
-1.52173913x + x2 = 0.5217391304

The x term is -1.52173913x.  Take half its coefficient (-0.760869565).
Square it (0.5789224949) and add it to both sides.

Add '0.5789224949' to each side of the equation.
-1.52173913x + 0.5789224949 + x2 = 0.5217391304 + 0.5789224949

Reorder the terms:
0.5789224949 + -1.52173913x + x2 = 0.5217391304 + 0.5789224949

Combine like terms: 0.5217391304 + 0.5789224949 = 1.1006616253
0.5789224949 + -1.52173913x + x2 = 1.1006616253

Factor a perfect square on the left side:
(x + -0.760869565)(x + -0.760869565) = 1.1006616253

Calculate the square root of the right side: 1.049124218

Break this problem into two subproblems by setting 
(x + -0.760869565) equal to 1.049124218 and -1.049124218.

Subproblem 1

x + -0.760869565 = 1.049124218 Simplifying x + -0.760869565 = 1.049124218 Reorder the terms: -0.760869565 + x = 1.049124218 Solving -0.760869565 + x = 1.049124218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.760869565' to each side of the equation. -0.760869565 + 0.760869565 + x = 1.049124218 + 0.760869565 Combine like terms: -0.760869565 + 0.760869565 = 0.000000000 0.000000000 + x = 1.049124218 + 0.760869565 x = 1.049124218 + 0.760869565 Combine like terms: 1.049124218 + 0.760869565 = 1.809993783 x = 1.809993783 Simplifying x = 1.809993783

Subproblem 2

x + -0.760869565 = -1.049124218 Simplifying x + -0.760869565 = -1.049124218 Reorder the terms: -0.760869565 + x = -1.049124218 Solving -0.760869565 + x = -1.049124218 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.760869565' to each side of the equation. -0.760869565 + 0.760869565 + x = -1.049124218 + 0.760869565 Combine like terms: -0.760869565 + 0.760869565 = 0.000000000 0.000000000 + x = -1.049124218 + 0.760869565 x = -1.049124218 + 0.760869565 Combine like terms: -1.049124218 + 0.760869565 = -0.288254653 x = -0.288254653 Simplifying x = -0.288254653

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.809993783, -0.288254653}

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