4-10x-50x^2=x^2

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Solution for 4-10x-50x^2=x^2 equation:


Simplifying
4 + -10x + -50x2 = x2

Solving
4 + -10x + -50x2 = x2

Solving for variable 'x'.

Combine like terms: -50x2 + -1x2 = -51x2
4 + -10x + -51x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
4 + -10x + -51x2 = 0

Begin completing the square.  Divide all terms by
-51 the coefficient of the squared term: 

Divide each side by '-51'.
-0.07843137255 + 0.1960784314x + x2 = 0

Move the constant term to the right:

Add '0.07843137255' to each side of the equation.
-0.07843137255 + 0.1960784314x + 0.07843137255 + x2 = 0 + 0.07843137255

Reorder the terms:
-0.07843137255 + 0.07843137255 + 0.1960784314x + x2 = 0 + 0.07843137255

Combine like terms: -0.07843137255 + 0.07843137255 = 0.00000000000
0.00000000000 + 0.1960784314x + x2 = 0 + 0.07843137255
0.1960784314x + x2 = 0 + 0.07843137255

Combine like terms: 0 + 0.07843137255 = 0.07843137255
0.1960784314x + x2 = 0.07843137255

The x term is 0.1960784314x.  Take half its coefficient (0.0980392157).
Square it (0.009611687815) and add it to both sides.

Add '0.009611687815' to each side of the equation.
0.1960784314x + 0.009611687815 + x2 = 0.07843137255 + 0.009611687815

Reorder the terms:
0.009611687815 + 0.1960784314x + x2 = 0.07843137255 + 0.009611687815

Combine like terms: 0.07843137255 + 0.009611687815 = 0.088043060365
0.009611687815 + 0.1960784314x + x2 = 0.088043060365

Factor a perfect square on the left side:
(x + 0.0980392157)(x + 0.0980392157) = 0.088043060365

Calculate the square root of the right side: 0.296720509

Break this problem into two subproblems by setting 
(x + 0.0980392157) equal to 0.296720509 and -0.296720509.

Subproblem 1

x + 0.0980392157 = 0.296720509 Simplifying x + 0.0980392157 = 0.296720509 Reorder the terms: 0.0980392157 + x = 0.296720509 Solving 0.0980392157 + x = 0.296720509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0980392157' to each side of the equation. 0.0980392157 + -0.0980392157 + x = 0.296720509 + -0.0980392157 Combine like terms: 0.0980392157 + -0.0980392157 = 0.0000000000 0.0000000000 + x = 0.296720509 + -0.0980392157 x = 0.296720509 + -0.0980392157 Combine like terms: 0.296720509 + -0.0980392157 = 0.1986812933 x = 0.1986812933 Simplifying x = 0.1986812933

Subproblem 2

x + 0.0980392157 = -0.296720509 Simplifying x + 0.0980392157 = -0.296720509 Reorder the terms: 0.0980392157 + x = -0.296720509 Solving 0.0980392157 + x = -0.296720509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0980392157' to each side of the equation. 0.0980392157 + -0.0980392157 + x = -0.296720509 + -0.0980392157 Combine like terms: 0.0980392157 + -0.0980392157 = 0.0000000000 0.0000000000 + x = -0.296720509 + -0.0980392157 x = -0.296720509 + -0.0980392157 Combine like terms: -0.296720509 + -0.0980392157 = -0.3947597247 x = -0.3947597247 Simplifying x = -0.3947597247

Solution

The solution to the problem is based on the solutions from the subproblems. x = {0.1986812933, -0.3947597247}

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