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Simplifying 0 = 6x2 + -30x + 100 Reorder the terms: 0 = 100 + -30x + 6x2 Solving 0 = 100 + -30x + 6x2 Solving for variable 'x'. Combine like terms: 0 + -100 = -100 -100 + 30x + -6x2 = 100 + -30x + 6x2 + -100 + 30x + -6x2 Reorder the terms: -100 + 30x + -6x2 = 100 + -100 + -30x + 30x + 6x2 + -6x2 Combine like terms: 100 + -100 = 0 -100 + 30x + -6x2 = 0 + -30x + 30x + 6x2 + -6x2 -100 + 30x + -6x2 = -30x + 30x + 6x2 + -6x2 Combine like terms: -30x + 30x = 0 -100 + 30x + -6x2 = 0 + 6x2 + -6x2 -100 + 30x + -6x2 = 6x2 + -6x2 Combine like terms: 6x2 + -6x2 = 0 -100 + 30x + -6x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-50 + 15x + -3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-50 + 15x + -3x2)' equal to zero and attempt to solve: Simplifying -50 + 15x + -3x2 = 0 Solving -50 + 15x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 16.66666667 + -5x + x2 = 0 Move the constant term to the right: Add '-16.66666667' to each side of the equation. 16.66666667 + -5x + -16.66666667 + x2 = 0 + -16.66666667 Reorder the terms: 16.66666667 + -16.66666667 + -5x + x2 = 0 + -16.66666667 Combine like terms: 16.66666667 + -16.66666667 = 0.00000000 0.00000000 + -5x + x2 = 0 + -16.66666667 -5x + x2 = 0 + -16.66666667 Combine like terms: 0 + -16.66666667 = -16.66666667 -5x + x2 = -16.66666667 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = -16.66666667 + 6.25 Reorder the terms: 6.25 + -5x + x2 = -16.66666667 + 6.25 Combine like terms: -16.66666667 + 6.25 = -10.41666667 6.25 + -5x + x2 = -10.41666667 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = -10.41666667 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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