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Simplifying -16t2 + 32t = 18 Reorder the terms: 32t + -16t2 = 18 Solving 32t + -16t2 = 18 Solving for variable 't'. Reorder the terms: -18 + 32t + -16t2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + 32t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-9 + 16t + -8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-9 + 16t + -8t2)' equal to zero and attempt to solve: Simplifying -9 + 16t + -8t2 = 0 Solving -9 + 16t + -8t2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. 1.125 + -2t + t2 = 0 Move the constant term to the right: Add '-1.125' to each side of the equation. 1.125 + -2t + -1.125 + t2 = 0 + -1.125 Reorder the terms: 1.125 + -1.125 + -2t + t2 = 0 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + -2t + t2 = 0 + -1.125 -2t + t2 = 0 + -1.125 Combine like terms: 0 + -1.125 = -1.125 -2t + t2 = -1.125 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 = -1.125 + 1 Reorder the terms: 1 + -2t + t2 = -1.125 + 1 Combine like terms: -1.125 + 1 = -0.125 1 + -2t + t2 = -0.125 Factor a perfect square on the left side: (t + -1)(t + -1) = -0.125 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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