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Simplifying -12t2 + 24t = 40 Reorder the terms: 24t + -12t2 = 40 Solving 24t + -12t2 = 40 Solving for variable 't'. Reorder the terms: -40 + 24t + -12t2 = 40 + -40 Combine like terms: 40 + -40 = 0 -40 + 24t + -12t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(-10 + 6t + -3t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-10 + 6t + -3t2)' equal to zero and attempt to solve: Simplifying -10 + 6t + -3t2 = 0 Solving -10 + 6t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 3.333333333 + -2t + t2 = 0 Move the constant term to the right: Add '-3.333333333' to each side of the equation. 3.333333333 + -2t + -3.333333333 + t2 = 0 + -3.333333333 Reorder the terms: 3.333333333 + -3.333333333 + -2t + t2 = 0 + -3.333333333 Combine like terms: 3.333333333 + -3.333333333 = 0.000000000 0.000000000 + -2t + t2 = 0 + -3.333333333 -2t + t2 = 0 + -3.333333333 Combine like terms: 0 + -3.333333333 = -3.333333333 -2t + t2 = -3.333333333 The t term is -2t. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2t + 1 + t2 = -3.333333333 + 1 Reorder the terms: 1 + -2t + t2 = -3.333333333 + 1 Combine like terms: -3.333333333 + 1 = -2.333333333 1 + -2t + t2 = -2.333333333 Factor a perfect square on the left side: (t + -1)(t + -1) = -2.333333333 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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