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Simplifying -5x(x + -1) = (4x + 2) * 3 Reorder the terms: -5x(-1 + x) = (4x + 2) * 3 (-1 * -5x + x * -5x) = (4x + 2) * 3 (5x + -5x2) = (4x + 2) * 3 Reorder the terms: 5x + -5x2 = (2 + 4x) * 3 Reorder the terms for easier multiplication: 5x + -5x2 = 3(2 + 4x) 5x + -5x2 = (2 * 3 + 4x * 3) 5x + -5x2 = (6 + 12x) Solving 5x + -5x2 = 6 + 12x Solving for variable 'x'. Reorder the terms: -6 + 5x + -12x + -5x2 = 6 + 12x + -6 + -12x Combine like terms: 5x + -12x = -7x -6 + -7x + -5x2 = 6 + 12x + -6 + -12x Reorder the terms: -6 + -7x + -5x2 = 6 + -6 + 12x + -12x Combine like terms: 6 + -6 = 0 -6 + -7x + -5x2 = 0 + 12x + -12x -6 + -7x + -5x2 = 12x + -12x Combine like terms: 12x + -12x = 0 -6 + -7x + -5x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(6 + 7x + 5x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(6 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 6 + 7x + 5x2 = 0 Solving 6 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.2 + 1.4x + x2 = 0 Move the constant term to the right: Add '-1.2' to each side of the equation. 1.2 + 1.4x + -1.2 + x2 = 0 + -1.2 Reorder the terms: 1.2 + -1.2 + 1.4x + x2 = 0 + -1.2 Combine like terms: 1.2 + -1.2 = 0.0 0.0 + 1.4x + x2 = 0 + -1.2 1.4x + x2 = 0 + -1.2 Combine like terms: 0 + -1.2 = -1.2 1.4x + x2 = -1.2 The x term is 1.4x. Take half its coefficient (0.7). Square it (0.49) and add it to both sides. Add '0.49' to each side of the equation. 1.4x + 0.49 + x2 = -1.2 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -1.2 + 0.49 Combine like terms: -1.2 + 0.49 = -0.71 0.49 + 1.4x + x2 = -0.71 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -0.71 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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