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Simplifying 30(2x + -1) = 6(x + 4) * 3x Reorder the terms: 30(-1 + 2x) = 6(x + 4) * 3x (-1 * 30 + 2x * 30) = 6(x + 4) * 3x (-30 + 60x) = 6(x + 4) * 3x Reorder the terms: -30 + 60x = 6(4 + x) * 3x Reorder the terms for easier multiplication: -30 + 60x = 6 * 3x(4 + x) Multiply 6 * 3 -30 + 60x = 18x(4 + x) -30 + 60x = (4 * 18x + x * 18x) -30 + 60x = (72x + 18x2) Solving -30 + 60x = 72x + 18x2 Solving for variable 'x'. Combine like terms: 60x + -72x = -12x -30 + -12x + -18x2 = 72x + 18x2 + -72x + -18x2 Reorder the terms: -30 + -12x + -18x2 = 72x + -72x + 18x2 + -18x2 Combine like terms: 72x + -72x = 0 -30 + -12x + -18x2 = 0 + 18x2 + -18x2 -30 + -12x + -18x2 = 18x2 + -18x2 Combine like terms: 18x2 + -18x2 = 0 -30 + -12x + -18x2 = 0 Factor out the Greatest Common Factor (GCF), '-6'. -6(5 + 2x + 3x2) = 0 Ignore the factor -6.Subproblem 1
Set the factor '(5 + 2x + 3x2)' equal to zero and attempt to solve: Simplifying 5 + 2x + 3x2 = 0 Solving 5 + 2x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 1.666666667 + 0.6666666667x + x2 = 0 Move the constant term to the right: Add '-1.666666667' to each side of the equation. 1.666666667 + 0.6666666667x + -1.666666667 + x2 = 0 + -1.666666667 Reorder the terms: 1.666666667 + -1.666666667 + 0.6666666667x + x2 = 0 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + 0.6666666667x + x2 = 0 + -1.666666667 0.6666666667x + x2 = 0 + -1.666666667 Combine like terms: 0 + -1.666666667 = -1.666666667 0.6666666667x + x2 = -1.666666667 The x term is 0.6666666667x. Take half its coefficient (0.3333333334). Square it (0.1111111112) and add it to both sides. Add '0.1111111112' to each side of the equation. 0.6666666667x + 0.1111111112 + x2 = -1.666666667 + 0.1111111112 Reorder the terms: 0.1111111112 + 0.6666666667x + x2 = -1.666666667 + 0.1111111112 Combine like terms: -1.666666667 + 0.1111111112 = -1.5555555558 0.1111111112 + 0.6666666667x + x2 = -1.5555555558 Factor a perfect square on the left side: (x + 0.3333333334)(x + 0.3333333334) = -1.5555555558 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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