0=3x^2+30x+117

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Solution for 0=3x^2+30x+117 equation:


Simplifying
0 = 3x2 + 30x + 117

Reorder the terms:
0 = 117 + 30x + 3x2

Solving
0 = 117 + 30x + 3x2

Solving for variable 'x'.

Combine like terms: 0 + -117 = -117
-117 + -30x + -3x2 = 117 + 30x + 3x2 + -117 + -30x + -3x2

Reorder the terms:
-117 + -30x + -3x2 = 117 + -117 + 30x + -30x + 3x2 + -3x2

Combine like terms: 117 + -117 = 0
-117 + -30x + -3x2 = 0 + 30x + -30x + 3x2 + -3x2
-117 + -30x + -3x2 = 30x + -30x + 3x2 + -3x2

Combine like terms: 30x + -30x = 0
-117 + -30x + -3x2 = 0 + 3x2 + -3x2
-117 + -30x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-117 + -30x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '-3'.
-3(39 + 10x + x2) = 0

Ignore the factor -3.

Subproblem 1

Set the factor '(39 + 10x + x2)' equal to zero and attempt to solve: Simplifying 39 + 10x + x2 = 0 Solving 39 + 10x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-39' to each side of the equation. 39 + 10x + -39 + x2 = 0 + -39 Reorder the terms: 39 + -39 + 10x + x2 = 0 + -39 Combine like terms: 39 + -39 = 0 0 + 10x + x2 = 0 + -39 10x + x2 = 0 + -39 Combine like terms: 0 + -39 = -39 10x + x2 = -39 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -39 + 25 Reorder the terms: 25 + 10x + x2 = -39 + 25 Combine like terms: -39 + 25 = -14 25 + 10x + x2 = -14 Factor a perfect square on the left side: (x + 5)(x + 5) = -14 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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