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Simplifying -3x(x + -1) + 9 = 15 Reorder the terms: -3x(-1 + x) + 9 = 15 (-1 * -3x + x * -3x) + 9 = 15 (3x + -3x2) + 9 = 15 Reorder the terms: 9 + 3x + -3x2 = 15 Solving 9 + 3x + -3x2 = 15 Solving for variable 'x'. Reorder the terms: 9 + -15 + 3x + -3x2 = 15 + -15 Combine like terms: 9 + -15 = -6 -6 + 3x + -3x2 = 15 + -15 Combine like terms: 15 + -15 = 0 -6 + 3x + -3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-2 + x + -1x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-2 + x + -1x2)' equal to zero and attempt to solve: Simplifying -2 + x + -1x2 = 0 Solving -2 + x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -1x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -1x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + -1x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1x + x2 = 0 + -2 -1x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 -1x + x2 = -2 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. -1x + 0.25 + x2 = -2 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -2 + 0.25 Combine like terms: -2 + 0.25 = -1.75 0.25 + -1x + x2 = -1.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = -1.75 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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