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Simplifying 36 = -16t2 + 36t + -10 Reorder the terms: 36 = -10 + 36t + -16t2 Solving 36 = -10 + 36t + -16t2 Solving for variable 't'. Combine like terms: 36 + 10 = 46 46 + -36t + 16t2 = -10 + 36t + -16t2 + 10 + -36t + 16t2 Reorder the terms: 46 + -36t + 16t2 = -10 + 10 + 36t + -36t + -16t2 + 16t2 Combine like terms: -10 + 10 = 0 46 + -36t + 16t2 = 0 + 36t + -36t + -16t2 + 16t2 46 + -36t + 16t2 = 36t + -36t + -16t2 + 16t2 Combine like terms: 36t + -36t = 0 46 + -36t + 16t2 = 0 + -16t2 + 16t2 46 + -36t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 46 + -36t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(23 + -18t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(23 + -18t + 8t2)' equal to zero and attempt to solve: Simplifying 23 + -18t + 8t2 = 0 Solving 23 + -18t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 2.875 + -2.25t + t2 = 0 Move the constant term to the right: Add '-2.875' to each side of the equation. 2.875 + -2.25t + -2.875 + t2 = 0 + -2.875 Reorder the terms: 2.875 + -2.875 + -2.25t + t2 = 0 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + -2.25t + t2 = 0 + -2.875 -2.25t + t2 = 0 + -2.875 Combine like terms: 0 + -2.875 = -2.875 -2.25t + t2 = -2.875 The t term is -2.25t. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25t + 1.265625 + t2 = -2.875 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = -2.875 + 1.265625 Combine like terms: -2.875 + 1.265625 = -1.609375 1.265625 + -2.25t + t2 = -1.609375 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = -1.609375 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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