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Simplifying 0 = 2t2 + 5t + 33 Reorder the terms: 0 = 33 + 5t + 2t2 Solving 0 = 33 + 5t + 2t2 Solving for variable 't'. Combine like terms: 0 + -33 = -33 -33 + -5t + -2t2 = 33 + 5t + 2t2 + -33 + -5t + -2t2 Reorder the terms: -33 + -5t + -2t2 = 33 + -33 + 5t + -5t + 2t2 + -2t2 Combine like terms: 33 + -33 = 0 -33 + -5t + -2t2 = 0 + 5t + -5t + 2t2 + -2t2 -33 + -5t + -2t2 = 5t + -5t + 2t2 + -2t2 Combine like terms: 5t + -5t = 0 -33 + -5t + -2t2 = 0 + 2t2 + -2t2 -33 + -5t + -2t2 = 2t2 + -2t2 Combine like terms: 2t2 + -2t2 = 0 -33 + -5t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(33 + 5t + 2t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(33 + 5t + 2t2)' equal to zero and attempt to solve: Simplifying 33 + 5t + 2t2 = 0 Solving 33 + 5t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 16.5 + 2.5t + t2 = 0 Move the constant term to the right: Add '-16.5' to each side of the equation. 16.5 + 2.5t + -16.5 + t2 = 0 + -16.5 Reorder the terms: 16.5 + -16.5 + 2.5t + t2 = 0 + -16.5 Combine like terms: 16.5 + -16.5 = 0.0 0.0 + 2.5t + t2 = 0 + -16.5 2.5t + t2 = 0 + -16.5 Combine like terms: 0 + -16.5 = -16.5 2.5t + t2 = -16.5 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = -16.5 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = -16.5 + 1.5625 Combine like terms: -16.5 + 1.5625 = -14.9375 1.5625 + 2.5t + t2 = -14.9375 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = -14.9375 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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