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Simplifying 6x(-3x + 3) + 6 = 21 Reorder the terms: 6x(3 + -3x) + 6 = 21 (3 * 6x + -3x * 6x) + 6 = 21 (18x + -18x2) + 6 = 21 Reorder the terms: 6 + 18x + -18x2 = 21 Solving 6 + 18x + -18x2 = 21 Solving for variable 'x'. Reorder the terms: 6 + -21 + 18x + -18x2 = 21 + -21 Combine like terms: 6 + -21 = -15 -15 + 18x + -18x2 = 21 + -21 Combine like terms: 21 + -21 = 0 -15 + 18x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-5 + 6x + -6x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-5 + 6x + -6x2)' equal to zero and attempt to solve: Simplifying -5 + 6x + -6x2 = 0 Solving -5 + 6x + -6x2 = 0 Begin completing the square. Divide all terms by -6 the coefficient of the squared term: Divide each side by '-6'. 0.8333333333 + -1x + x2 = 0 Move the constant term to the right: Add '-0.8333333333' to each side of the equation. 0.8333333333 + -1x + -0.8333333333 + x2 = 0 + -0.8333333333 Reorder the terms: 0.8333333333 + -0.8333333333 + -1x + x2 = 0 + -0.8333333333 Combine like terms: 0.8333333333 + -0.8333333333 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + -0.8333333333 -1x + x2 = 0 + -0.8333333333 Combine like terms: 0 + -0.8333333333 = -0.8333333333 -1x + x2 = -0.8333333333 The x term is -1x. 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 = -0.8333333333 + 0.25 Reorder the terms: 0.25 + -1x + x2 = -0.8333333333 + 0.25 Combine like terms: -0.8333333333 + 0.25 = -0.5833333333 0.25 + -1x + x2 = -0.5833333333 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = -0.5833333333 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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