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Simplifying -2t(t + 5) = 15 + -7t Reorder the terms: -2t(5 + t) = 15 + -7t (5 * -2t + t * -2t) = 15 + -7t (-10t + -2t2) = 15 + -7t Solving -10t + -2t2 = 15 + -7t Solving for variable 't'. Reorder the terms: -15 + -10t + 7t + -2t2 = 15 + -7t + -15 + 7t Combine like terms: -10t + 7t = -3t -15 + -3t + -2t2 = 15 + -7t + -15 + 7t Reorder the terms: -15 + -3t + -2t2 = 15 + -15 + -7t + 7t Combine like terms: 15 + -15 = 0 -15 + -3t + -2t2 = 0 + -7t + 7t -15 + -3t + -2t2 = -7t + 7t Combine like terms: -7t + 7t = 0 -15 + -3t + -2t2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(15 + 3t + 2t2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(15 + 3t + 2t2)' equal to zero and attempt to solve: Simplifying 15 + 3t + 2t2 = 0 Solving 15 + 3t + 2t2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 7.5 + 1.5t + t2 = 0 Move the constant term to the right: Add '-7.5' to each side of the equation. 7.5 + 1.5t + -7.5 + t2 = 0 + -7.5 Reorder the terms: 7.5 + -7.5 + 1.5t + t2 = 0 + -7.5 Combine like terms: 7.5 + -7.5 = 0.0 0.0 + 1.5t + t2 = 0 + -7.5 1.5t + t2 = 0 + -7.5 Combine like terms: 0 + -7.5 = -7.5 1.5t + t2 = -7.5 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 = -7.5 + 0.5625 Reorder the terms: 0.5625 + 1.5t + t2 = -7.5 + 0.5625 Combine like terms: -7.5 + 0.5625 = -6.9375 0.5625 + 1.5t + t2 = -6.9375 Factor a perfect square on the left side: (t + 0.75)(t + 0.75) = -6.9375 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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