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Simplifying x = 3000 + 20x2 + 20x Reorder the terms: x = 3000 + 20x + 20x2 Solving x = 3000 + 20x + 20x2 Solving for variable 'x'. Reorder the terms: -3000 + x + -20x + -20x2 = 3000 + 20x + 20x2 + -3000 + -20x + -20x2 Combine like terms: x + -20x = -19x -3000 + -19x + -20x2 = 3000 + 20x + 20x2 + -3000 + -20x + -20x2 Reorder the terms: -3000 + -19x + -20x2 = 3000 + -3000 + 20x + -20x + 20x2 + -20x2 Combine like terms: 3000 + -3000 = 0 -3000 + -19x + -20x2 = 0 + 20x + -20x + 20x2 + -20x2 -3000 + -19x + -20x2 = 20x + -20x + 20x2 + -20x2 Combine like terms: 20x + -20x = 0 -3000 + -19x + -20x2 = 0 + 20x2 + -20x2 -3000 + -19x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -3000 + -19x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3000 + 19x + 20x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3000 + 19x + 20x2)' equal to zero and attempt to solve: Simplifying 3000 + 19x + 20x2 = 0 Solving 3000 + 19x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 150 + 0.95x + x2 = 0.0 Move the constant term to the right: Add '-150' to each side of the equation. 150 + 0.95x + -150 + x2 = 0.0 + -150 Reorder the terms: 150 + -150 + 0.95x + x2 = 0.0 + -150 Combine like terms: 150 + -150 = 0 0 + 0.95x + x2 = 0.0 + -150 0.95x + x2 = 0.0 + -150 Combine like terms: 0.0 + -150 = -150 0.95x + x2 = -150 The x term is 0.95x. Take half its coefficient (0.475). Square it (0.225625) and add it to both sides. Add '0.225625' to each side of the equation. 0.95x + 0.225625 + x2 = -150 + 0.225625 Reorder the terms: 0.225625 + 0.95x + x2 = -150 + 0.225625 Combine like terms: -150 + 0.225625 = -149.774375 0.225625 + 0.95x + x2 = -149.774375 Factor a perfect square on the left side: (x + 0.475)(x + 0.475) = -149.774375 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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