-0.27x^2+3.3x+77=80

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Solution for -0.27x^2+3.3x+77=80 equation:


Simplifying
-0.27x2 + 3.3x + 77 = 80

Reorder the terms:
77 + 3.3x + -0.27x2 = 80

Solving
77 + 3.3x + -0.27x2 = 80

Solving for variable 'x'.

Reorder the terms:
77 + -80 + 3.3x + -0.27x2 = 80 + -80

Combine like terms: 77 + -80 = -3
-3 + 3.3x + -0.27x2 = 80 + -80

Combine like terms: 80 + -80 = 0
-3 + 3.3x + -0.27x2 = 0

Begin completing the square.  Divide all terms by
-0.27 the coefficient of the squared term: 

Divide each side by '-0.27'.
11.11111111 + -12.22222222x + x2 = 0

Move the constant term to the right:

Add '-11.11111111' to each side of the equation.
11.11111111 + -12.22222222x + -11.11111111 + x2 = 0 + -11.11111111

Reorder the terms:
11.11111111 + -11.11111111 + -12.22222222x + x2 = 0 + -11.11111111

Combine like terms: 11.11111111 + -11.11111111 = 0.00000000
0.00000000 + -12.22222222x + x2 = 0 + -11.11111111
-12.22222222x + x2 = 0 + -11.11111111

Combine like terms: 0 + -11.11111111 = -11.11111111
-12.22222222x + x2 = -11.11111111

The x term is -12.22222222x.  Take half its coefficient (-6.11111111).
Square it (37.34567900) and add it to both sides.

Add '37.34567900' to each side of the equation.
-12.22222222x + 37.34567900 + x2 = -11.11111111 + 37.34567900

Reorder the terms:
37.34567900 + -12.22222222x + x2 = -11.11111111 + 37.34567900

Combine like terms: -11.11111111 + 37.34567900 = 26.23456789
37.34567900 + -12.22222222x + x2 = 26.23456789

Factor a perfect square on the left side:
(x + -6.11111111)(x + -6.11111111) = 26.23456789

Calculate the square root of the right side: 5.121969142

Break this problem into two subproblems by setting 
(x + -6.11111111) equal to 5.121969142 and -5.121969142.

Subproblem 1

x + -6.11111111 = 5.121969142 Simplifying x + -6.11111111 = 5.121969142 Reorder the terms: -6.11111111 + x = 5.121969142 Solving -6.11111111 + x = 5.121969142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.11111111' to each side of the equation. -6.11111111 + 6.11111111 + x = 5.121969142 + 6.11111111 Combine like terms: -6.11111111 + 6.11111111 = 0.00000000 0.00000000 + x = 5.121969142 + 6.11111111 x = 5.121969142 + 6.11111111 Combine like terms: 5.121969142 + 6.11111111 = 11.233080252 x = 11.233080252 Simplifying x = 11.233080252

Subproblem 2

x + -6.11111111 = -5.121969142 Simplifying x + -6.11111111 = -5.121969142 Reorder the terms: -6.11111111 + x = -5.121969142 Solving -6.11111111 + x = -5.121969142 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6.11111111' to each side of the equation. -6.11111111 + 6.11111111 + x = -5.121969142 + 6.11111111 Combine like terms: -6.11111111 + 6.11111111 = 0.00000000 0.00000000 + x = -5.121969142 + 6.11111111 x = -5.121969142 + 6.11111111 Combine like terms: -5.121969142 + 6.11111111 = 0.989141968 x = 0.989141968 Simplifying x = 0.989141968

Solution

The solution to the problem is based on the solutions from the subproblems. x = {11.233080252, 0.989141968}

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