66530=.65x^2-.047x+2

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Solution for 66530=.65x^2-.047x+2 equation:


Simplifying
66530 = 0.65x2 + -0.047x + 2

Reorder the terms:
66530 = 2 + -0.047x + 0.65x2

Solving
66530 = 2 + -0.047x + 0.65x2

Solving for variable 'x'.

Combine like terms: 66530 + -2 = 66528
66528 + 0.047x + -0.65x2 = 2 + -0.047x + 0.65x2 + -2 + 0.047x + -0.65x2

Reorder the terms:
66528 + 0.047x + -0.65x2 = 2 + -2 + -0.047x + 0.047x + 0.65x2 + -0.65x2

Combine like terms: 2 + -2 = 0
66528 + 0.047x + -0.65x2 = 0 + -0.047x + 0.047x + 0.65x2 + -0.65x2
66528 + 0.047x + -0.65x2 = -0.047x + 0.047x + 0.65x2 + -0.65x2

Combine like terms: -0.047x + 0.047x = 0.000
66528 + 0.047x + -0.65x2 = 0.000 + 0.65x2 + -0.65x2
66528 + 0.047x + -0.65x2 = 0.65x2 + -0.65x2

Combine like terms: 0.65x2 + -0.65x2 = 0.00
66528 + 0.047x + -0.65x2 = 0.00

Begin completing the square.  Divide all terms by
-0.65 the coefficient of the squared term: 

Divide each side by '-0.65'.
-102350.7692 + -0.07230769231x + x2 = 0

Move the constant term to the right:

Add '102350.7692' to each side of the equation.
-102350.7692 + -0.07230769231x + 102350.7692 + x2 = 0 + 102350.7692

Reorder the terms:
-102350.7692 + 102350.7692 + -0.07230769231x + x2 = 0 + 102350.7692

Combine like terms: -102350.7692 + 102350.7692 = 0.0000
0.0000 + -0.07230769231x + x2 = 0 + 102350.7692
-0.07230769231x + x2 = 0 + 102350.7692

Combine like terms: 0 + 102350.7692 = 102350.7692
-0.07230769231x + x2 = 102350.7692

The x term is -0.07230769231x.  Take half its coefficient (-0.03615384616).
Square it (0.001307100592) and add it to both sides.

Add '0.001307100592' to each side of the equation.
-0.07230769231x + 0.001307100592 + x2 = 102350.7692 + 0.001307100592

Reorder the terms:
0.001307100592 + -0.07230769231x + x2 = 102350.7692 + 0.001307100592

Combine like terms: 102350.7692 + 0.001307100592 = 102350.770507100592
0.001307100592 + -0.07230769231x + x2 = 102350.770507100592

Factor a perfect square on the left side:
(x + -0.03615384616)(x + -0.03615384616) = 102350.770507100592

Calculate the square root of the right side: 319.92306967

Break this problem into two subproblems by setting 
(x + -0.03615384616) equal to 319.92306967 and -319.92306967.

Subproblem 1

x + -0.03615384616 = 319.92306967 Simplifying x + -0.03615384616 = 319.92306967 Reorder the terms: -0.03615384616 + x = 319.92306967 Solving -0.03615384616 + x = 319.92306967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03615384616' to each side of the equation. -0.03615384616 + 0.03615384616 + x = 319.92306967 + 0.03615384616 Combine like terms: -0.03615384616 + 0.03615384616 = 0.00000000000 0.00000000000 + x = 319.92306967 + 0.03615384616 x = 319.92306967 + 0.03615384616 Combine like terms: 319.92306967 + 0.03615384616 = 319.95922351616 x = 319.95922351616 Simplifying x = 319.95922351616

Subproblem 2

x + -0.03615384616 = -319.92306967 Simplifying x + -0.03615384616 = -319.92306967 Reorder the terms: -0.03615384616 + x = -319.92306967 Solving -0.03615384616 + x = -319.92306967 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.03615384616' to each side of the equation. -0.03615384616 + 0.03615384616 + x = -319.92306967 + 0.03615384616 Combine like terms: -0.03615384616 + 0.03615384616 = 0.00000000000 0.00000000000 + x = -319.92306967 + 0.03615384616 x = -319.92306967 + 0.03615384616 Combine like terms: -319.92306967 + 0.03615384616 = -319.88691582384 x = -319.88691582384 Simplifying x = -319.88691582384

Solution

The solution to the problem is based on the solutions from the subproblems. x = {319.95922351616, -319.88691582384}

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