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Simplifying 4(-4x + 5) = 6x(5 + -6x) Reorder the terms: 4(5 + -4x) = 6x(5 + -6x) (5 * 4 + -4x * 4) = 6x(5 + -6x) (20 + -16x) = 6x(5 + -6x) 20 + -16x = (5 * 6x + -6x * 6x) 20 + -16x = (30x + -36x2) Solving 20 + -16x = 30x + -36x2 Solving for variable 'x'. Combine like terms: -16x + -30x = -46x 20 + -46x + 36x2 = 30x + -36x2 + -30x + 36x2 Reorder the terms: 20 + -46x + 36x2 = 30x + -30x + -36x2 + 36x2 Combine like terms: 30x + -30x = 0 20 + -46x + 36x2 = 0 + -36x2 + 36x2 20 + -46x + 36x2 = -36x2 + 36x2 Combine like terms: -36x2 + 36x2 = 0 20 + -46x + 36x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(10 + -23x + 18x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(10 + -23x + 18x2)' equal to zero and attempt to solve: Simplifying 10 + -23x + 18x2 = 0 Solving 10 + -23x + 18x2 = 0 Begin completing the square. Divide all terms by 18 the coefficient of the squared term: Divide each side by '18'. 0.5555555556 + -1.277777778x + x2 = 0 Move the constant term to the right: Add '-0.5555555556' to each side of the equation. 0.5555555556 + -1.277777778x + -0.5555555556 + x2 = 0 + -0.5555555556 Reorder the terms: 0.5555555556 + -0.5555555556 + -1.277777778x + x2 = 0 + -0.5555555556 Combine like terms: 0.5555555556 + -0.5555555556 = 0.0000000000 0.0000000000 + -1.277777778x + x2 = 0 + -0.5555555556 -1.277777778x + x2 = 0 + -0.5555555556 Combine like terms: 0 + -0.5555555556 = -0.5555555556 -1.277777778x + x2 = -0.5555555556 The x term is -1.277777778x. Take half its coefficient (-0.638888889). Square it (0.4081790125) and add it to both sides. Add '0.4081790125' to each side of the equation. -1.277777778x + 0.4081790125 + x2 = -0.5555555556 + 0.4081790125 Reorder the terms: 0.4081790125 + -1.277777778x + x2 = -0.5555555556 + 0.4081790125 Combine like terms: -0.5555555556 + 0.4081790125 = -0.1473765431 0.4081790125 + -1.277777778x + x2 = -0.1473765431 Factor a perfect square on the left side: (x + -0.638888889)(x + -0.638888889) = -0.1473765431 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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