195x^2-16x=87

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Solution for 195x^2-16x=87 equation:


Simplifying
195x2 + -16x = 87

Reorder the terms:
-16x + 195x2 = 87

Solving
-16x + 195x2 = 87

Solving for variable 'x'.

Reorder the terms:
-87 + -16x + 195x2 = 87 + -87

Combine like terms: 87 + -87 = 0
-87 + -16x + 195x2 = 0

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

Divide each side by '195'.
-0.4461538462 + -0.08205128205x + x2 = 0

Move the constant term to the right:

Add '0.4461538462' to each side of the equation.
-0.4461538462 + -0.08205128205x + 0.4461538462 + x2 = 0 + 0.4461538462

Reorder the terms:
-0.4461538462 + 0.4461538462 + -0.08205128205x + x2 = 0 + 0.4461538462

Combine like terms: -0.4461538462 + 0.4461538462 = 0.0000000000
0.0000000000 + -0.08205128205x + x2 = 0 + 0.4461538462
-0.08205128205x + x2 = 0 + 0.4461538462

Combine like terms: 0 + 0.4461538462 = 0.4461538462
-0.08205128205x + x2 = 0.4461538462

The x term is -0.08205128205x.  Take half its coefficient (-0.04102564103).
Square it (0.001683103222) and add it to both sides.

Add '0.001683103222' to each side of the equation.
-0.08205128205x + 0.001683103222 + x2 = 0.4461538462 + 0.001683103222

Reorder the terms:
0.001683103222 + -0.08205128205x + x2 = 0.4461538462 + 0.001683103222

Combine like terms: 0.4461538462 + 0.001683103222 = 0.447836949422
0.001683103222 + -0.08205128205x + x2 = 0.447836949422

Factor a perfect square on the left side:
(x + -0.04102564103)(x + -0.04102564103) = 0.447836949422

Calculate the square root of the right side: 0.669206208

Break this problem into two subproblems by setting 
(x + -0.04102564103) equal to 0.669206208 and -0.669206208.

Subproblem 1

x + -0.04102564103 = 0.669206208 Simplifying x + -0.04102564103 = 0.669206208 Reorder the terms: -0.04102564103 + x = 0.669206208 Solving -0.04102564103 + x = 0.669206208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04102564103' to each side of the equation. -0.04102564103 + 0.04102564103 + x = 0.669206208 + 0.04102564103 Combine like terms: -0.04102564103 + 0.04102564103 = 0.00000000000 0.00000000000 + x = 0.669206208 + 0.04102564103 x = 0.669206208 + 0.04102564103 Combine like terms: 0.669206208 + 0.04102564103 = 0.71023184903 x = 0.71023184903 Simplifying x = 0.71023184903

Subproblem 2

x + -0.04102564103 = -0.669206208 Simplifying x + -0.04102564103 = -0.669206208 Reorder the terms: -0.04102564103 + x = -0.669206208 Solving -0.04102564103 + x = -0.669206208 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.04102564103' to each side of the equation. -0.04102564103 + 0.04102564103 + x = -0.669206208 + 0.04102564103 Combine like terms: -0.04102564103 + 0.04102564103 = 0.00000000000 0.00000000000 + x = -0.669206208 + 0.04102564103 x = -0.669206208 + 0.04102564103 Combine like terms: -0.669206208 + 0.04102564103 = -0.62818056697 x = -0.62818056697 Simplifying x = -0.62818056697

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.71023184903, -0.62818056697}

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