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Simplifying 0 = 2t2 + 3t + 20 Reorder the terms: 0 = 20 + 3t + 2t2 Solving 0 = 20 + 3t + 2t2 Solving for variable 't'. Combine like terms: 0 + -20 = -20 -20 + -3t + -2t2 = 20 + 3t + 2t2 + -20 + -3t + -2t2 Reorder the terms: -20 + -3t + -2t2 = 20 + -20 + 3t + -3t + 2t2 + -2t2 Combine like terms: 20 + -20 = 0 -20 + -3t + -2t2 = 0 + 3t + -3t + 2t2 + -2t2 -20 + -3t + -2t2 = 3t + -3t + 2t2 + -2t2 Combine like terms: 3t + -3t = 0 -20 + -3t + -2t2 = 0 + 2t2 + -2t2 -20 + -3t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -20 + -3t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(20 + 3t + 2t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(20 + 3t + 2t2)' equal to zero and attempt to solve: Simplifying 20 + 3t + 2t2 = 0 Solving 20 + 3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 10 + 1.5t + t2 = 0 Move the constant term to the right: Add '-10' to each side of the equation. 10 + 1.5t + -10 + t2 = 0 + -10 Reorder the terms: 10 + -10 + 1.5t + t2 = 0 + -10 Combine like terms: 10 + -10 = 0 0 + 1.5t + t2 = 0 + -10 1.5t + t2 = 0 + -10 Combine like terms: 0 + -10 = -10 1.5t + t2 = -10 The t term is 1.5t. Take half its coefficient (0.75). Square it (0.5625) and add it to both sides. Add '0.5625' to each side of the equation. 1.5t + 0.5625 + t2 = -10 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -10 + 0.5625 Combine like terms: -10 + 0.5625 = -9.4375 0.5625 + 1.5t + t2 = -9.4375 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -9.4375 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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