49.3x^2-64x+19.2=0

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Solution for 49.3x^2-64x+19.2=0 equation:


Simplifying
49.3x2 + -64x + 19.2 = 0

Reorder the terms:
19.2 + -64x + 49.3x2 = 0

Solving
19.2 + -64x + 49.3x2 = 0

Solving for variable 'x'.

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

Divide each side by '49.3'.
0.3894523327 + -1.298174442x + x2 = 0

Move the constant term to the right:

Add '-0.3894523327' to each side of the equation.
0.3894523327 + -1.298174442x + -0.3894523327 + x2 = 0 + -0.3894523327

Reorder the terms:
0.3894523327 + -0.3894523327 + -1.298174442x + x2 = 0 + -0.3894523327

Combine like terms: 0.3894523327 + -0.3894523327 = 0.0000000000
0.0000000000 + -1.298174442x + x2 = 0 + -0.3894523327
-1.298174442x + x2 = 0 + -0.3894523327

Combine like terms: 0 + -0.3894523327 = -0.3894523327
-1.298174442x + x2 = -0.3894523327

The x term is -1.298174442x.  Take half its coefficient (-0.649087221).
Square it (0.4213142205) and add it to both sides.

Add '0.4213142205' to each side of the equation.
-1.298174442x + 0.4213142205 + x2 = -0.3894523327 + 0.4213142205

Reorder the terms:
0.4213142205 + -1.298174442x + x2 = -0.3894523327 + 0.4213142205

Combine like terms: -0.3894523327 + 0.4213142205 = 0.0318618878
0.4213142205 + -1.298174442x + x2 = 0.0318618878

Factor a perfect square on the left side:
(x + -0.649087221)(x + -0.649087221) = 0.0318618878

Calculate the square root of the right side: 0.178498985

Break this problem into two subproblems by setting 
(x + -0.649087221) equal to 0.178498985 and -0.178498985.

Subproblem 1

x + -0.649087221 = 0.178498985 Simplifying x + -0.649087221 = 0.178498985 Reorder the terms: -0.649087221 + x = 0.178498985 Solving -0.649087221 + x = 0.178498985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.649087221' to each side of the equation. -0.649087221 + 0.649087221 + x = 0.178498985 + 0.649087221 Combine like terms: -0.649087221 + 0.649087221 = 0.000000000 0.000000000 + x = 0.178498985 + 0.649087221 x = 0.178498985 + 0.649087221 Combine like terms: 0.178498985 + 0.649087221 = 0.827586206 x = 0.827586206 Simplifying x = 0.827586206

Subproblem 2

x + -0.649087221 = -0.178498985 Simplifying x + -0.649087221 = -0.178498985 Reorder the terms: -0.649087221 + x = -0.178498985 Solving -0.649087221 + x = -0.178498985 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.649087221' to each side of the equation. -0.649087221 + 0.649087221 + x = -0.178498985 + 0.649087221 Combine like terms: -0.649087221 + 0.649087221 = 0.000000000 0.000000000 + x = -0.178498985 + 0.649087221 x = -0.178498985 + 0.649087221 Combine like terms: -0.178498985 + 0.649087221 = 0.470588236 x = 0.470588236 Simplifying x = 0.470588236

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.827586206, 0.470588236}

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