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Simplifying -16t2 + 36t + 15 = 0 Reorder the terms: 15 + 36t + -16t2 = 0 Solving 15 + 36t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.9375 + -2.25t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -2.25t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -2.25t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -2.25t + t2 = 0 + 0.9375 -2.25t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -2.25t + t2 = 0.9375 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 = 0.9375 + 1.265625 Reorder the terms: 1.265625 + -2.25t + t2 = 0.9375 + 1.265625 Combine like terms: 0.9375 + 1.265625 = 2.203125 1.265625 + -2.25t + t2 = 2.203125 Factor a perfect square on the left side: (t + -1.125)(t + -1.125) = 2.203125 Calculate the square root of the right side: 1.484292761 Break this problem into two subproblems by setting (t + -1.125) equal to 1.484292761 and -1.484292761.Subproblem 1
t + -1.125 = 1.484292761 Simplifying t + -1.125 = 1.484292761 Reorder the terms: -1.125 + t = 1.484292761 Solving -1.125 + t = 1.484292761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = 1.484292761 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = 1.484292761 + 1.125 t = 1.484292761 + 1.125 Combine like terms: 1.484292761 + 1.125 = 2.609292761 t = 2.609292761 Simplifying t = 2.609292761Subproblem 2
t + -1.125 = -1.484292761 Simplifying t + -1.125 = -1.484292761 Reorder the terms: -1.125 + t = -1.484292761 Solving -1.125 + t = -1.484292761 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + t = -1.484292761 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + t = -1.484292761 + 1.125 t = -1.484292761 + 1.125 Combine like terms: -1.484292761 + 1.125 = -0.359292761 t = -0.359292761 Simplifying t = -0.359292761Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.609292761, -0.359292761}
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