-4.9x^2+30.5x+9.1=0

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Solution for -4.9x^2+30.5x+9.1=0 equation:


Simplifying
-4.9x2 + 30.5x + 9.1 = 0

Reorder the terms:
9.1 + 30.5x + -4.9x2 = 0

Solving
9.1 + 30.5x + -4.9x2 = 0

Solving for variable 'x'.

Begin completing the square.  Divide all terms by
-4.9 the coefficient of the squared term: 

Divide each side by '-4.9'.
-1.857142857 + -6.224489796x + x2 = 0

Move the constant term to the right:

Add '1.857142857' to each side of the equation.
-1.857142857 + -6.224489796x + 1.857142857 + x2 = 0 + 1.857142857

Reorder the terms:
-1.857142857 + 1.857142857 + -6.224489796x + x2 = 0 + 1.857142857

Combine like terms: -1.857142857 + 1.857142857 = 0.000000000
0.000000000 + -6.224489796x + x2 = 0 + 1.857142857
-6.224489796x + x2 = 0 + 1.857142857

Combine like terms: 0 + 1.857142857 = 1.857142857
-6.224489796x + x2 = 1.857142857

The x term is -6.224489796x.  Take half its coefficient (-3.112244898).
Square it (9.686068305) and add it to both sides.

Add '9.686068305' to each side of the equation.
-6.224489796x + 9.686068305 + x2 = 1.857142857 + 9.686068305

Reorder the terms:
9.686068305 + -6.224489796x + x2 = 1.857142857 + 9.686068305

Combine like terms: 1.857142857 + 9.686068305 = 11.543211162
9.686068305 + -6.224489796x + x2 = 11.543211162

Factor a perfect square on the left side:
(x + -3.112244898)(x + -3.112244898) = 11.543211162

Calculate the square root of the right side: 3.397530156

Break this problem into two subproblems by setting 
(x + -3.112244898) equal to 3.397530156 and -3.397530156.

Subproblem 1

x + -3.112244898 = 3.397530156 Simplifying x + -3.112244898 = 3.397530156 Reorder the terms: -3.112244898 + x = 3.397530156 Solving -3.112244898 + x = 3.397530156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + x = 3.397530156 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + x = 3.397530156 + 3.112244898 x = 3.397530156 + 3.112244898 Combine like terms: 3.397530156 + 3.112244898 = 6.509775054 x = 6.509775054 Simplifying x = 6.509775054

Subproblem 2

x + -3.112244898 = -3.397530156 Simplifying x + -3.112244898 = -3.397530156 Reorder the terms: -3.112244898 + x = -3.397530156 Solving -3.112244898 + x = -3.397530156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.112244898' to each side of the equation. -3.112244898 + 3.112244898 + x = -3.397530156 + 3.112244898 Combine like terms: -3.112244898 + 3.112244898 = 0.000000000 0.000000000 + x = -3.397530156 + 3.112244898 x = -3.397530156 + 3.112244898 Combine like terms: -3.397530156 + 3.112244898 = -0.285285258 x = -0.285285258 Simplifying x = -0.285285258

Solution

The solution to the problem is based on the solutions from the subproblems. x = {6.509775054, -0.285285258}

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