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Simplifying 6x(x + 3) + -5(6x + -4) = 0 Reorder the terms: 6x(3 + x) + -5(6x + -4) = 0 (3 * 6x + x * 6x) + -5(6x + -4) = 0 (18x + 6x2) + -5(6x + -4) = 0 Reorder the terms: 18x + 6x2 + -5(-4 + 6x) = 0 18x + 6x2 + (-4 * -5 + 6x * -5) = 0 18x + 6x2 + (20 + -30x) = 0 Reorder the terms: 20 + 18x + -30x + 6x2 = 0 Combine like terms: 18x + -30x = -12x 20 + -12x + 6x2 = 0 Solving 20 + -12x + 6x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -6x + 3x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -6x + 3x2)' equal to zero and attempt to solve: Simplifying 10 + -6x + 3x2 = 0 Solving 10 + -6x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 3.333333333 + -2x + x2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -2x + -3.333333333 + x2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -2x + x2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -2x + x2 = 0 + -3.333333333 -2x + x2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -2x + x2 = -3.333333333 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 = -3.333333333 + 1 Reorder the terms: 1 + -2x + x2 = -3.333333333 + 1 Combine like terms: -3.333333333 + 1 = -2.333333333 1 + -2x + x2 = -2.333333333 Factor a perfect square on the left side: (x + -1)(x + -1) = -2.333333333 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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