5.10x+25.8x^2=1050.6

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Solution for 5.10x+25.8x^2=1050.6 equation:


Simplifying
5.10x + 25.8x2 = 1050.6

Solving
5.10x + 25.8x2 = 1050.6

Solving for variable 'x'.

Reorder the terms:
-1050.6 + 5.10x + 25.8x2 = 1050.6 + -1050.6

Combine like terms: 1050.6 + -1050.6 = 0.0
-1050.6 + 5.10x + 25.8x2 = 0.0

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

Divide each side by '25.8'.
-40.72093023 + 0.1976744186x + x2 = 0

Move the constant term to the right:

Add '40.72093023' to each side of the equation.
-40.72093023 + 0.1976744186x + 40.72093023 + x2 = 0 + 40.72093023

Reorder the terms:
-40.72093023 + 40.72093023 + 0.1976744186x + x2 = 0 + 40.72093023

Combine like terms: -40.72093023 + 40.72093023 = 0.00000000
0.00000000 + 0.1976744186x + x2 = 0 + 40.72093023
0.1976744186x + x2 = 0 + 40.72093023

Combine like terms: 0 + 40.72093023 = 40.72093023
0.1976744186x + x2 = 40.72093023

The x term is 0.1976744186x.  Take half its coefficient (0.0988372093).
Square it (0.009768793942) and add it to both sides.

Add '0.009768793942' to each side of the equation.
0.1976744186x + 0.009768793942 + x2 = 40.72093023 + 0.009768793942

Reorder the terms:
0.009768793942 + 0.1976744186x + x2 = 40.72093023 + 0.009768793942

Combine like terms: 40.72093023 + 0.009768793942 = 40.730699023942
0.009768793942 + 0.1976744186x + x2 = 40.730699023942

Factor a perfect square on the left side:
(x + 0.0988372093)(x + 0.0988372093) = 40.730699023942

Calculate the square root of the right side: 6.382060719

Break this problem into two subproblems by setting 
(x + 0.0988372093) equal to 6.382060719 and -6.382060719.

Subproblem 1

x + 0.0988372093 = 6.382060719 Simplifying x + 0.0988372093 = 6.382060719 Reorder the terms: 0.0988372093 + x = 6.382060719 Solving 0.0988372093 + x = 6.382060719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0988372093' to each side of the equation. 0.0988372093 + -0.0988372093 + x = 6.382060719 + -0.0988372093 Combine like terms: 0.0988372093 + -0.0988372093 = 0.0000000000 0.0000000000 + x = 6.382060719 + -0.0988372093 x = 6.382060719 + -0.0988372093 Combine like terms: 6.382060719 + -0.0988372093 = 6.2832235097 x = 6.2832235097 Simplifying x = 6.2832235097

Subproblem 2

x + 0.0988372093 = -6.382060719 Simplifying x + 0.0988372093 = -6.382060719 Reorder the terms: 0.0988372093 + x = -6.382060719 Solving 0.0988372093 + x = -6.382060719 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.0988372093' to each side of the equation. 0.0988372093 + -0.0988372093 + x = -6.382060719 + -0.0988372093 Combine like terms: 0.0988372093 + -0.0988372093 = 0.0000000000 0.0000000000 + x = -6.382060719 + -0.0988372093 x = -6.382060719 + -0.0988372093 Combine like terms: -6.382060719 + -0.0988372093 = -6.4808979283 x = -6.4808979283 Simplifying x = -6.4808979283

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.2832235097, -6.4808979283}

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