-4.6x^2-3x+20=0

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Solution for -4.6x^2-3x+20=0 equation:


Simplifying
-4.6x2 + -3x + 20 = 0

Reorder the terms:
20 + -3x + -4.6x2 = 0

Solving
20 + -3x + -4.6x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.6 the coefficient of the squared term: 

Divide each side by '-4.6'.
-4.347826087 + 0.652173913x + x2 = 0

Move the constant term to the right:

Add '4.347826087' to each side of the equation.
-4.347826087 + 0.652173913x + 4.347826087 + x2 = 0 + 4.347826087

Reorder the terms:
-4.347826087 + 4.347826087 + 0.652173913x + x2 = 0 + 4.347826087

Combine like terms: -4.347826087 + 4.347826087 = 0.000000000
0.000000000 + 0.652173913x + x2 = 0 + 4.347826087
0.652173913x + x2 = 0 + 4.347826087

Combine like terms: 0 + 4.347826087 = 4.347826087
0.652173913x + x2 = 4.347826087

The x term is 0.652173913x.  Take half its coefficient (0.3260869565).
Square it (0.1063327032) and add it to both sides.

Add '0.1063327032' to each side of the equation.
0.652173913x + 0.1063327032 + x2 = 4.347826087 + 0.1063327032

Reorder the terms:
0.1063327032 + 0.652173913x + x2 = 4.347826087 + 0.1063327032

Combine like terms: 4.347826087 + 0.1063327032 = 4.4541587902
0.1063327032 + 0.652173913x + x2 = 4.4541587902

Factor a perfect square on the left side:
(x + 0.3260869565)(x + 0.3260869565) = 4.4541587902

Calculate the square root of the right side: 2.110487809

Break this problem into two subproblems by setting 
(x + 0.3260869565) equal to 2.110487809 and -2.110487809.

Subproblem 1

x + 0.3260869565 = 2.110487809 Simplifying x + 0.3260869565 = 2.110487809 Reorder the terms: 0.3260869565 + x = 2.110487809 Solving 0.3260869565 + x = 2.110487809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3260869565' to each side of the equation. 0.3260869565 + -0.3260869565 + x = 2.110487809 + -0.3260869565 Combine like terms: 0.3260869565 + -0.3260869565 = 0.0000000000 0.0000000000 + x = 2.110487809 + -0.3260869565 x = 2.110487809 + -0.3260869565 Combine like terms: 2.110487809 + -0.3260869565 = 1.7844008525 x = 1.7844008525 Simplifying x = 1.7844008525

Subproblem 2

x + 0.3260869565 = -2.110487809 Simplifying x + 0.3260869565 = -2.110487809 Reorder the terms: 0.3260869565 + x = -2.110487809 Solving 0.3260869565 + x = -2.110487809 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3260869565' to each side of the equation. 0.3260869565 + -0.3260869565 + x = -2.110487809 + -0.3260869565 Combine like terms: 0.3260869565 + -0.3260869565 = 0.0000000000 0.0000000000 + x = -2.110487809 + -0.3260869565 x = -2.110487809 + -0.3260869565 Combine like terms: -2.110487809 + -0.3260869565 = -2.4365747655 x = -2.4365747655 Simplifying x = -2.4365747655

Solution

The solution to the problem is based on the solutions from the subproblems. x = {1.7844008525, -2.4365747655}

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