65529+2x=5x^2

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Solution for 65529+2x=5x^2 equation:


Simplifying
65529 + 2x = 5x2

Solving
65529 + 2x = 5x2

Solving for variable 'x'.

Combine like terms: 5x2 + -5x2 = 0
65529 + 2x + -5x2 = 0

Begin completing the square.  Divide all terms by
-5 the coefficient of the squared term: 

Divide each side by '-5'.
-13105.8 + -0.4x + x2 = 0

Move the constant term to the right:

Add '13105.8' to each side of the equation.
-13105.8 + -0.4x + 13105.8 + x2 = 0 + 13105.8

Reorder the terms:
-13105.8 + 13105.8 + -0.4x + x2 = 0 + 13105.8

Combine like terms: -13105.8 + 13105.8 = 0.0
0.0 + -0.4x + x2 = 0 + 13105.8
-0.4x + x2 = 0 + 13105.8

Combine like terms: 0 + 13105.8 = 13105.8
-0.4x + x2 = 13105.8

The x term is -0.4x.  Take half its coefficient (-0.2).
Square it (0.04) and add it to both sides.

Add '0.04' to each side of the equation.
-0.4x + 0.04 + x2 = 13105.8 + 0.04

Reorder the terms:
0.04 + -0.4x + x2 = 13105.8 + 0.04

Combine like terms: 13105.8 + 0.04 = 13105.84
0.04 + -0.4x + x2 = 13105.84

Factor a perfect square on the left side:
(x + -0.2)(x + -0.2) = 13105.84

Calculate the square root of the right side: 114.480740738

Break this problem into two subproblems by setting 
(x + -0.2) equal to 114.480740738 and -114.480740738.

Subproblem 1

x + -0.2 = 114.480740738 Simplifying x + -0.2 = 114.480740738 Reorder the terms: -0.2 + x = 114.480740738 Solving -0.2 + x = 114.480740738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = 114.480740738 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = 114.480740738 + 0.2 x = 114.480740738 + 0.2 Combine like terms: 114.480740738 + 0.2 = 114.680740738 x = 114.680740738 Simplifying x = 114.680740738

Subproblem 2

x + -0.2 = -114.480740738 Simplifying x + -0.2 = -114.480740738 Reorder the terms: -0.2 + x = -114.480740738 Solving -0.2 + x = -114.480740738 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + x = -114.480740738 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + x = -114.480740738 + 0.2 x = -114.480740738 + 0.2 Combine like terms: -114.480740738 + 0.2 = -114.280740738 x = -114.280740738 Simplifying x = -114.280740738

Solution

The solution to the problem is based on the solutions from the subproblems. x = {114.680740738, -114.280740738}

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