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Simplifying 5x(-4x + 2) = 13x + 9 Reorder the terms: 5x(2 + -4x) = 13x + 9 (2 * 5x + -4x * 5x) = 13x + 9 (10x + -20x2) = 13x + 9 Reorder the terms: 10x + -20x2 = 9 + 13x Solving 10x + -20x2 = 9 + 13x Solving for variable 'x'. Reorder the terms: -9 + 10x + -13x + -20x2 = 9 + 13x + -9 + -13x Combine like terms: 10x + -13x = -3x -9 + -3x + -20x2 = 9 + 13x + -9 + -13x Reorder the terms: -9 + -3x + -20x2 = 9 + -9 + 13x + -13x Combine like terms: 9 + -9 = 0 -9 + -3x + -20x2 = 0 + 13x + -13x -9 + -3x + -20x2 = 13x + -13x Combine like terms: 13x + -13x = 0 -9 + -3x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(9 + 3x + 20x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(9 + 3x + 20x2)' equal to zero and attempt to solve: Simplifying 9 + 3x + 20x2 = 0 Solving 9 + 3x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 0.45 + 0.15x + x2 = 0.0 Move the constant term to the right: Add '-0.45' to each side of the equation. 0.45 + 0.15x + -0.45 + x2 = 0.0 + -0.45 Reorder the terms: 0.45 + -0.45 + 0.15x + x2 = 0.0 + -0.45 Combine like terms: 0.45 + -0.45 = 0.00 0.00 + 0.15x + x2 = 0.0 + -0.45 0.15x + x2 = 0.0 + -0.45 Combine like terms: 0.0 + -0.45 = -0.45 0.15x + x2 = -0.45 The x term is 0.15x. Take half its coefficient (0.075). Square it (0.005625) and add it to both sides. Add '0.005625' to each side of the equation. 0.15x + 0.005625 + x2 = -0.45 + 0.005625 Reorder the terms: 0.005625 + 0.15x + x2 = -0.45 + 0.005625 Combine like terms: -0.45 + 0.005625 = -0.444375 0.005625 + 0.15x + x2 = -0.444375 Factor a perfect square on the left side: (x + 0.075)(x + 0.075) = -0.444375 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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