0=9x^2+3x+5

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Solution for 0=9x^2+3x+5 equation:


Simplifying
0 = 9x2 + 3x + 5

Reorder the terms:
0 = 5 + 3x + 9x2

Solving
0 = 5 + 3x + 9x2

Solving for variable 'x'.

Combine like terms: 0 + -5 = -5
-5 + -3x + -9x2 = 5 + 3x + 9x2 + -5 + -3x + -9x2

Reorder the terms:
-5 + -3x + -9x2 = 5 + -5 + 3x + -3x + 9x2 + -9x2

Combine like terms: 5 + -5 = 0
-5 + -3x + -9x2 = 0 + 3x + -3x + 9x2 + -9x2
-5 + -3x + -9x2 = 3x + -3x + 9x2 + -9x2

Combine like terms: 3x + -3x = 0
-5 + -3x + -9x2 = 0 + 9x2 + -9x2
-5 + -3x + -9x2 = 9x2 + -9x2

Combine like terms: 9x2 + -9x2 = 0
-5 + -3x + -9x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(5 + 3x + 9x2) = 0

Ignore the factor -1.

Subproblem 1

Set the factor '(5 + 3x + 9x2)' equal to zero and attempt to solve: Simplifying 5 + 3x + 9x2 = 0 Solving 5 + 3x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. 0.5555555556 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + 0.3333333333x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + 0.3333333333x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + 0.3333333333x + x2 = 0 + -0.5555555556 0.3333333333x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 0.3333333333x + x2 = -0.5555555556 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.5555555556 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.5555555556 + 0.02777777779 Combine like terms: -0.5555555556 + 0.02777777779 = -0.52777777781 0.02777777779 + 0.3333333333x + x2 = -0.52777777781 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = -0.52777777781 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.

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