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Simplifying 0 = 3x2 + -6x + 15 Reorder the terms: 0 = 15 + -6x + 3x2 Solving 0 = 15 + -6x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -15 = -15 -15 + 6x + -3x2 = 15 + -6x + 3x2 + -15 + 6x + -3x2 Reorder the terms: -15 + 6x + -3x2 = 15 + -15 + -6x + 6x + 3x2 + -3x2 Combine like terms: 15 + -15 = 0 -15 + 6x + -3x2 = 0 + -6x + 6x + 3x2 + -3x2 -15 + 6x + -3x2 = -6x + 6x + 3x2 + -3x2 Combine like terms: -6x + 6x = 0 -15 + 6x + -3x2 = 0 + 3x2 + -3x2 -15 + 6x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -15 + 6x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 2x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 2x + -1x2)' equal to zero and attempt to solve: Simplifying -5 + 2x + -1x2 = 0 Solving -5 + 2x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 5 + -2x + x2 = 0 Move the constant term to the right: Add '-5' to each side of the equation. 5 + -2x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -2x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -2x + x2 = 0 + -5 -2x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -2x + x2 = -5 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 = -5 + 1 Reorder the terms: 1 + -2x + x2 = -5 + 1 Combine like terms: -5 + 1 = -4 1 + -2x + x2 = -4 Factor a perfect square on the left side: (x + -1)(x + -1) = -4 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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