0=27x^2+54x+90

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Solution for 0=27x^2+54x+90 equation:


Simplifying
0 = 27x2 + 54x + 90

Reorder the terms:
0 = 90 + 54x + 27x2

Solving
0 = 90 + 54x + 27x2

Solving for variable 'x'.

Combine like terms: 0 + -90 = -90
-90 + -54x + -27x2 = 90 + 54x + 27x2 + -90 + -54x + -27x2

Reorder the terms:
-90 + -54x + -27x2 = 90 + -90 + 54x + -54x + 27x2 + -27x2

Combine like terms: 90 + -90 = 0
-90 + -54x + -27x2 = 0 + 54x + -54x + 27x2 + -27x2
-90 + -54x + -27x2 = 54x + -54x + 27x2 + -27x2

Combine like terms: 54x + -54x = 0
-90 + -54x + -27x2 = 0 + 27x2 + -27x2
-90 + -54x + -27x2 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
-90 + -54x + -27x2 = 0

Factor out the Greatest Common Factor (GCF), '-9'.
-9(10 + 6x + 3x2) = 0

Ignore the factor -9.

Subproblem 1

Set the factor '(10 + 6x + 3x2)' equal to zero and attempt to solve: Simplifying 10 + 6x + 3x2 = 0 Solving 10 + 6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + 2x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + 2x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + 2x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + 2x + x2 = 0 + -3.333333333 2x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 2x + x2 = -3.333333333 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = -3.333333333 + 1 Reorder the terms: 1 + 2x + x2 = -3.333333333 + 1 Combine like terms: -3.333333333 + 1 = -2.333333333 1 + 2x + x2 = -2.333333333 Factor a perfect square on the left side: (x + 1)(x + 1) = -2.333333333 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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