5x+5=30x^2+15+5

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Solution for 5x+5=30x^2+15+5 equation:


Simplifying
5x + 5 = 30x2 + 15 + 5

Reorder the terms:
5 + 5x = 30x2 + 15 + 5

Reorder the terms:
5 + 5x = 15 + 5 + 30x2

Combine like terms: 15 + 5 = 20
5 + 5x = 20 + 30x2

Solving
5 + 5x = 20 + 30x2

Solving for variable 'x'.

Reorder the terms:
5 + -20 + 5x + -30x2 = 20 + 30x2 + -20 + -30x2

Combine like terms: 5 + -20 = -15
-15 + 5x + -30x2 = 20 + 30x2 + -20 + -30x2

Reorder the terms:
-15 + 5x + -30x2 = 20 + -20 + 30x2 + -30x2

Combine like terms: 20 + -20 = 0
-15 + 5x + -30x2 = 0 + 30x2 + -30x2
-15 + 5x + -30x2 = 30x2 + -30x2

Combine like terms: 30x2 + -30x2 = 0
-15 + 5x + -30x2 = 0

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + x + -6x2) = 0

Ignore the factor 5.

Subproblem 1

Set the factor '(-3 + x + -6x2)' equal to zero and attempt to solve: Simplifying -3 + x + -6x2 = 0 Solving -3 + x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.5 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + -0.1666666667x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + -0.1666666667x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + -0.1666666667x + x2 = 0 + -0.5 -0.1666666667x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 -0.1666666667x + x2 = -0.5 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -0.1666666667x + 0.25 + x2 = -0.5 + 0.25 Reorder the terms: 0.25 + -0.1666666667x + x2 = -0.5 + 0.25 Combine like terms: -0.5 + 0.25 = -0.25 0.25 + -0.1666666667x + x2 = -0.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -0.25 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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