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Simplifying 0 = 20x2 + 29x + 20 Reorder the terms: 0 = 20 + 29x + 20x2 Solving 0 = 20 + 29x + 20x2 Solving for variable 'x'. Combine like terms: 0 + -20 = -20 -20 + -29x + -20x2 = 20 + 29x + 20x2 + -20 + -29x + -20x2 Reorder the terms: -20 + -29x + -20x2 = 20 + -20 + 29x + -29x + 20x2 + -20x2 Combine like terms: 20 + -20 = 0 -20 + -29x + -20x2 = 0 + 29x + -29x + 20x2 + -20x2 -20 + -29x + -20x2 = 29x + -29x + 20x2 + -20x2 Combine like terms: 29x + -29x = 0 -20 + -29x + -20x2 = 0 + 20x2 + -20x2 -20 + -29x + -20x2 = 20x2 + -20x2 Combine like terms: 20x2 + -20x2 = 0 -20 + -29x + -20x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 29x + 20x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 29x + 20x2)' equal to zero and attempt to solve: Simplifying 20 + 29x + 20x2 = 0 Solving 20 + 29x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. 1 + 1.45x + x2 = 0.0 Move the constant term to the right: Add '-1' to each side of the equation. 1 + 1.45x + -1 + x2 = 0.0 + -1 Reorder the terms: 1 + -1 + 1.45x + x2 = 0.0 + -1 Combine like terms: 1 + -1 = 0 0 + 1.45x + x2 = 0.0 + -1 1.45x + x2 = 0.0 + -1 Combine like terms: 0.0 + -1 = -1 1.45x + x2 = -1 The x term is 1.45x. Take half its coefficient (0.725). Square it (0.525625) and add it to both sides. Add '0.525625' to each side of the equation. 1.45x + 0.525625 + x2 = -1 + 0.525625 Reorder the terms: 0.525625 + 1.45x + x2 = -1 + 0.525625 Combine like terms: -1 + 0.525625 = -0.474375 0.525625 + 1.45x + x2 = -0.474375 Factor a perfect square on the left side: (x + 0.725)(x + 0.725) = -0.474375 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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