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Simplifying 18 + -10x + 10(3x + 4 + 3x) + -20 + 10x(2x + -12 + 3x) = 0 Reorder the terms: 18 + -10x + 10(4 + 3x + 3x) + -20 + 10x(2x + -12 + 3x) = 0 Combine like terms: 3x + 3x = 6x 18 + -10x + 10(4 + 6x) + -20 + 10x(2x + -12 + 3x) = 0 18 + -10x + (4 * 10 + 6x * 10) + -20 + 10x(2x + -12 + 3x) = 0 18 + -10x + (40 + 60x) + -20 + 10x(2x + -12 + 3x) = 0 Reorder the terms: 18 + -10x + 40 + 60x + -20 + 10x(-12 + 2x + 3x) = 0 Combine like terms: 2x + 3x = 5x 18 + -10x + 40 + 60x + -20 + 10x(-12 + 5x) = 0 18 + -10x + 40 + 60x + -20 + (-12 * 10x + 5x * 10x) = 0 18 + -10x + 40 + 60x + -20 + (-120x + 50x2) = 0 Reorder the terms: 18 + 40 + -20 + -10x + 60x + -120x + 50x2 = 0 Combine like terms: 18 + 40 = 58 58 + -20 + -10x + 60x + -120x + 50x2 = 0 Combine like terms: 58 + -20 = 38 38 + -10x + 60x + -120x + 50x2 = 0 Combine like terms: -10x + 60x = 50x 38 + 50x + -120x + 50x2 = 0 Combine like terms: 50x + -120x = -70x 38 + -70x + 50x2 = 0 Solving 38 + -70x + 50x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(19 + -35x + 25x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(19 + -35x + 25x2)' equal to zero and attempt to solve: Simplifying 19 + -35x + 25x2 = 0 Solving 19 + -35x + 25x2 = 0 Begin completing the square. Divide all terms by 25 the coefficient of the squared term: Divide each side by '25'. 0.76 + -1.4x + x2 = 0 Move the constant term to the right: Add '-0.76' to each side of the equation. 0.76 + -1.4x + -0.76 + x2 = 0 + -0.76 Reorder the terms: 0.76 + -0.76 + -1.4x + x2 = 0 + -0.76 Combine like terms: 0.76 + -0.76 = 0.00 0.00 + -1.4x + x2 = 0 + -0.76 -1.4x + x2 = 0 + -0.76 Combine like terms: 0 + -0.76 = -0.76 -1.4x + x2 = -0.76 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 = -0.76 + 0.49 Reorder the terms: 0.49 + -1.4x + x2 = -0.76 + 0.49 Combine like terms: -0.76 + 0.49 = -0.27 0.49 + -1.4x + x2 = -0.27 Factor a perfect square on the left side: (x + -0.7)(x + -0.7) = -0.27 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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