27x+x^2=506.16

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Solution for 27x+x^2=506.16 equation:


Simplifying
27x + x2 = 506.16

Solving
27x + x2 = 506.16

Solving for variable 'x'.

Reorder the terms:
-506.16 + 27x + x2 = 506.16 + -506.16

Combine like terms: 506.16 + -506.16 = 0.00
-506.16 + 27x + x2 = 0.00

Begin completing the square.

Move the constant term to the right:

Add '506.16' to each side of the equation.
-506.16 + 27x + 506.16 + x2 = 0.00 + 506.16

Reorder the terms:
-506.16 + 506.16 + 27x + x2 = 0.00 + 506.16

Combine like terms: -506.16 + 506.16 = 0.00
0.00 + 27x + x2 = 0.00 + 506.16
27x + x2 = 0.00 + 506.16

Combine like terms: 0.00 + 506.16 = 506.16
27x + x2 = 506.16

The x term is 27x.  Take half its coefficient (13.5).
Square it (182.25) and add it to both sides.

Add '182.25' to each side of the equation.
27x + 182.25 + x2 = 506.16 + 182.25

Reorder the terms:
182.25 + 27x + x2 = 506.16 + 182.25

Combine like terms: 506.16 + 182.25 = 688.41
182.25 + 27x + x2 = 688.41

Factor a perfect square on the left side:
(x + 13.5)(x + 13.5) = 688.41

Calculate the square root of the right side: 26.237568485

Break this problem into two subproblems by setting 
(x + 13.5) equal to 26.237568485 and -26.237568485.

Subproblem 1

x + 13.5 = 26.237568485 Simplifying x + 13.5 = 26.237568485 Reorder the terms: 13.5 + x = 26.237568485 Solving 13.5 + x = 26.237568485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = 26.237568485 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = 26.237568485 + -13.5 x = 26.237568485 + -13.5 Combine like terms: 26.237568485 + -13.5 = 12.737568485 x = 12.737568485 Simplifying x = 12.737568485

Subproblem 2

x + 13.5 = -26.237568485 Simplifying x + 13.5 = -26.237568485 Reorder the terms: 13.5 + x = -26.237568485 Solving 13.5 + x = -26.237568485 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.5' to each side of the equation. 13.5 + -13.5 + x = -26.237568485 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + x = -26.237568485 + -13.5 x = -26.237568485 + -13.5 Combine like terms: -26.237568485 + -13.5 = -39.737568485 x = -39.737568485 Simplifying x = -39.737568485

Solution

The solution to the problem is based on the solutions from the subproblems. x = {12.737568485, -39.737568485}

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