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Simplifying -4(-3x + -5) = -1(10x + 8) * 2x Reorder the terms: -4(-5 + -3x) = -1(10x + 8) * 2x (-5 * -4 + -3x * -4) = -1(10x + 8) * 2x (20 + 12x) = -1(10x + 8) * 2x Reorder the terms: 20 + 12x = -1(8 + 10x) * 2x Reorder the terms for easier multiplication: 20 + 12x = -1 * 2x(8 + 10x) Multiply -1 * 2 20 + 12x = -2x(8 + 10x) 20 + 12x = (8 * -2x + 10x * -2x) 20 + 12x = (-16x + -20x2) Solving 20 + 12x = -16x + -20x2 Solving for variable 'x'. Combine like terms: 12x + 16x = 28x 20 + 28x + 20x2 = -16x + -20x2 + 16x + 20x2 Reorder the terms: 20 + 28x + 20x2 = -16x + 16x + -20x2 + 20x2 Combine like terms: -16x + 16x = 0 20 + 28x + 20x2 = 0 + -20x2 + 20x2 20 + 28x + 20x2 = -20x2 + 20x2 Combine like terms: -20x2 + 20x2 = 0 20 + 28x + 20x2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(5 + 7x + 5x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(5 + 7x + 5x2)' equal to zero and attempt to solve: Simplifying 5 + 7x + 5x2 = 0 Solving 5 + 7x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1 + 1.4x + x2 = 0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.4x + -1 + x2 = 0 + -1 Reorder the terms: 1 + -1 + 1.4x + x2 = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.4x + x2 = 0 + -1 1.4x + x2 = 0 + -1 Combine like terms: 0 + -1 = -1 1.4x + x2 = -1 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 + 0.49 Reorder the terms: 0.49 + 1.4x + x2 = -1 + 0.49 Combine like terms: -1 + 0.49 = -0.51 0.49 + 1.4x + x2 = -0.51 Factor a perfect square on the left side: (x + 0.7)(x + 0.7) = -0.51 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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