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Simplifying -10x + -40x(2 + -5x) = 60(x + -2) + -28 -10x + (2 * -40x + -5x * -40x) = 60(x + -2) + -28 -10x + (-80x + 200x2) = 60(x + -2) + -28 Combine like terms: -10x + -80x = -90x -90x + 200x2 = 60(x + -2) + -28 Reorder the terms: -90x + 200x2 = 60(-2 + x) + -28 -90x + 200x2 = (-2 * 60 + x * 60) + -28 -90x + 200x2 = (-120 + 60x) + -28 Reorder the terms: -90x + 200x2 = -120 + -28 + 60x Combine like terms: -120 + -28 = -148 -90x + 200x2 = -148 + 60x Solving -90x + 200x2 = -148 + 60x Solving for variable 'x'. Reorder the terms: 148 + -90x + -60x + 200x2 = -148 + 60x + 148 + -60x Combine like terms: -90x + -60x = -150x 148 + -150x + 200x2 = -148 + 60x + 148 + -60x Reorder the terms: 148 + -150x + 200x2 = -148 + 148 + 60x + -60x Combine like terms: -148 + 148 = 0 148 + -150x + 200x2 = 0 + 60x + -60x 148 + -150x + 200x2 = 60x + -60x Combine like terms: 60x + -60x = 0 148 + -150x + 200x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(74 + -75x + 100x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(74 + -75x + 100x2)' equal to zero and attempt to solve: Simplifying 74 + -75x + 100x2 = 0 Solving 74 + -75x + 100x2 = 0 Begin completing the square. Divide all terms by 100 the coefficient of the squared term: Divide each side by '100'. 0.74 + -0.75x + x2 = 0.00 Move the constant term to the right: Add '-0.74' to each side of the equation. 0.74 + -0.75x + -0.74 + x2 = 0.00 + -0.74 Reorder the terms: 0.74 + -0.74 + -0.75x + x2 = 0.00 + -0.74 Combine like terms: 0.74 + -0.74 = 0.00 0.00 + -0.75x + x2 = 0.00 + -0.74 -0.75x + x2 = 0.00 + -0.74 Combine like terms: 0.00 + -0.74 = -0.74 -0.75x + x2 = -0.74 The x term is -0.75x. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75x + 0.140625 + x2 = -0.74 + 0.140625 Reorder the terms: 0.140625 + -0.75x + x2 = -0.74 + 0.140625 Combine like terms: -0.74 + 0.140625 = -0.599375 0.140625 + -0.75x + x2 = -0.599375 Factor a perfect square on the left side: (x + -0.375)(x + -0.375) = -0.599375 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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