50+4x-0.03x^2=0

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Solution for 50+4x-0.03x^2=0 equation:


Simplifying
50 + 4x + -0.03x2 = 0

Solving
50 + 4x + -0.03x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-0.03 the coefficient of the squared term: 

Divide each side by '-0.03'.
-1666.666667 + -133.3333333x + x2 = 0

Move the constant term to the right:

Add '1666.666667' to each side of the equation.
-1666.666667 + -133.3333333x + 1666.666667 + x2 = 0 + 1666.666667

Reorder the terms:
-1666.666667 + 1666.666667 + -133.3333333x + x2 = 0 + 1666.666667

Combine like terms: -1666.666667 + 1666.666667 = 0.000000
0.000000 + -133.3333333x + x2 = 0 + 1666.666667
-133.3333333x + x2 = 0 + 1666.666667

Combine like terms: 0 + 1666.666667 = 1666.666667
-133.3333333x + x2 = 1666.666667

The x term is -133.3333333x.  Take half its coefficient (-66.66666665).
Square it (4444.444442) and add it to both sides.

Add '4444.444442' to each side of the equation.
-133.3333333x + 4444.444442 + x2 = 1666.666667 + 4444.444442

Reorder the terms:
4444.444442 + -133.3333333x + x2 = 1666.666667 + 4444.444442

Combine like terms: 1666.666667 + 4444.444442 = 6111.111109
4444.444442 + -133.3333333x + x2 = 6111.111109

Factor a perfect square on the left side:
(x + -66.66666665)(x + -66.66666665) = 6111.111109

Calculate the square root of the right side: 78.173595984

Break this problem into two subproblems by setting 
(x + -66.66666665) equal to 78.173595984 and -78.173595984.

Subproblem 1

x + -66.66666665 = 78.173595984 Simplifying x + -66.66666665 = 78.173595984 Reorder the terms: -66.66666665 + x = 78.173595984 Solving -66.66666665 + x = 78.173595984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = 78.173595984 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = 78.173595984 + 66.66666665 x = 78.173595984 + 66.66666665 Combine like terms: 78.173595984 + 66.66666665 = 144.840262634 x = 144.840262634 Simplifying x = 144.840262634

Subproblem 2

x + -66.66666665 = -78.173595984 Simplifying x + -66.66666665 = -78.173595984 Reorder the terms: -66.66666665 + x = -78.173595984 Solving -66.66666665 + x = -78.173595984 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '66.66666665' to each side of the equation. -66.66666665 + 66.66666665 + x = -78.173595984 + 66.66666665 Combine like terms: -66.66666665 + 66.66666665 = 0.00000000 0.00000000 + x = -78.173595984 + 66.66666665 x = -78.173595984 + 66.66666665 Combine like terms: -78.173595984 + 66.66666665 = -11.506929334 x = -11.506929334 Simplifying x = -11.506929334

Solution

The solution to the problem is based on the solutions from the subproblems. x = {144.840262634, -11.506929334}

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