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Simplifying 0 = 16t2 + 15t + -15 Reorder the terms: 0 = -15 + 15t + 16t2 Solving 0 = -15 + 15t + 16t2 Solving for variable 't'. Combine like terms: 0 + 15 = 15 15 + -15t + -16t2 = -15 + 15t + 16t2 + 15 + -15t + -16t2 Reorder the terms: 15 + -15t + -16t2 = -15 + 15 + 15t + -15t + 16t2 + -16t2 Combine like terms: -15 + 15 = 0 15 + -15t + -16t2 = 0 + 15t + -15t + 16t2 + -16t2 15 + -15t + -16t2 = 15t + -15t + 16t2 + -16t2 Combine like terms: 15t + -15t = 0 15 + -15t + -16t2 = 0 + 16t2 + -16t2 15 + -15t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 15 + -15t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.9375 + 0.9375t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 0.9375t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 0.9375t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 0.9375t + t2 = 0 + 0.9375 0.9375t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 0.9375t + t2 = 0.9375 The t term is 0.9375t. Take half its coefficient (0.46875). Square it (0.2197265625) and add it to both sides. Add '0.2197265625' to each side of the equation. 0.9375t + 0.2197265625 + t2 = 0.9375 + 0.2197265625 Reorder the terms: 0.2197265625 + 0.9375t + t2 = 0.9375 + 0.2197265625 Combine like terms: 0.9375 + 0.2197265625 = 1.1572265625 0.2197265625 + 0.9375t + t2 = 1.1572265625 Factor a perfect square on the left side: (t + 0.46875)(t + 0.46875) = 1.1572265625 Calculate the square root of the right side: 1.075744655 Break this problem into two subproblems by setting (t + 0.46875) equal to 1.075744655 and -1.075744655.Subproblem 1
t + 0.46875 = 1.075744655 Simplifying t + 0.46875 = 1.075744655 Reorder the terms: 0.46875 + t = 1.075744655 Solving 0.46875 + t = 1.075744655 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = 1.075744655 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = 1.075744655 + -0.46875 t = 1.075744655 + -0.46875 Combine like terms: 1.075744655 + -0.46875 = 0.606994655 t = 0.606994655 Simplifying t = 0.606994655Subproblem 2
t + 0.46875 = -1.075744655 Simplifying t + 0.46875 = -1.075744655 Reorder the terms: 0.46875 + t = -1.075744655 Solving 0.46875 + t = -1.075744655 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.46875' to each side of the equation. 0.46875 + -0.46875 + t = -1.075744655 + -0.46875 Combine like terms: 0.46875 + -0.46875 = 0.00000 0.00000 + t = -1.075744655 + -0.46875 t = -1.075744655 + -0.46875 Combine like terms: -1.075744655 + -0.46875 = -1.544494655 t = -1.544494655 Simplifying t = -1.544494655Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.606994655, -1.544494655}
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