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Simplifying -16t2 + 18t + 15 = 0 Reorder the terms: 15 + 18t + -16t2 = 0 Solving 15 + 18t + -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 + -1.125t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -1.125t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -1.125t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -1.125t + t2 = 0 + 0.9375 -1.125t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -1.125t + t2 = 0.9375 The t term is -1.125t. Take half its coefficient (-0.5625). Square it (0.31640625) and add it to both sides. Add '0.31640625' to each side of the equation. -1.125t + 0.31640625 + t2 = 0.9375 + 0.31640625 Reorder the terms: 0.31640625 + -1.125t + t2 = 0.9375 + 0.31640625 Combine like terms: 0.9375 + 0.31640625 = 1.25390625 0.31640625 + -1.125t + t2 = 1.25390625 Factor a perfect square on the left side: (t + -0.5625)(t + -0.5625) = 1.25390625 Calculate the square root of the right side: 1.119779554 Break this problem into two subproblems by setting (t + -0.5625) equal to 1.119779554 and -1.119779554.Subproblem 1
t + -0.5625 = 1.119779554 Simplifying t + -0.5625 = 1.119779554 Reorder the terms: -0.5625 + t = 1.119779554 Solving -0.5625 + t = 1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = 1.119779554 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = 1.119779554 + 0.5625 t = 1.119779554 + 0.5625 Combine like terms: 1.119779554 + 0.5625 = 1.682279554 t = 1.682279554 Simplifying t = 1.682279554Subproblem 2
t + -0.5625 = -1.119779554 Simplifying t + -0.5625 = -1.119779554 Reorder the terms: -0.5625 + t = -1.119779554 Solving -0.5625 + t = -1.119779554 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5625' to each side of the equation. -0.5625 + 0.5625 + t = -1.119779554 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + t = -1.119779554 + 0.5625 t = -1.119779554 + 0.5625 Combine like terms: -1.119779554 + 0.5625 = -0.557279554 t = -0.557279554 Simplifying t = -0.557279554Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.682279554, -0.557279554}
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