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Simplifying -16t2 + 15t + 68 = 0 Reorder the terms: 68 + 15t + -16t2 = 0 Solving 68 + 15t + -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'. -4.25 + -0.9375t + t2 = 0 Move the constant term to the right: Add '4.25' to each side of the equation. -4.25 + -0.9375t + 4.25 + t2 = 0 + 4.25 Reorder the terms: -4.25 + 4.25 + -0.9375t + t2 = 0 + 4.25 Combine like terms: -4.25 + 4.25 = 0.00 0.00 + -0.9375t + t2 = 0 + 4.25 -0.9375t + t2 = 0 + 4.25 Combine like terms: 0 + 4.25 = 4.25 -0.9375t + t2 = 4.25 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 = 4.25 + 0.2197265625 Reorder the terms: 0.2197265625 + -0.9375t + t2 = 4.25 + 0.2197265625 Combine like terms: 4.25 + 0.2197265625 = 4.4697265625 0.2197265625 + -0.9375t + t2 = 4.4697265625 Factor a perfect square on the left side: (t + -0.46875)(t + -0.46875) = 4.4697265625 Calculate the square root of the right side: 2.114172784 Break this problem into two subproblems by setting (t + -0.46875) equal to 2.114172784 and -2.114172784.Subproblem 1
t + -0.46875 = 2.114172784 Simplifying t + -0.46875 = 2.114172784 Reorder the terms: -0.46875 + t = 2.114172784 Solving -0.46875 + t = 2.114172784 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 = 2.114172784 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = 2.114172784 + 0.46875 t = 2.114172784 + 0.46875 Combine like terms: 2.114172784 + 0.46875 = 2.582922784 t = 2.582922784 Simplifying t = 2.582922784Subproblem 2
t + -0.46875 = -2.114172784 Simplifying t + -0.46875 = -2.114172784 Reorder the terms: -0.46875 + t = -2.114172784 Solving -0.46875 + t = -2.114172784 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 = -2.114172784 + 0.46875 Combine like terms: -0.46875 + 0.46875 = 0.00000 0.00000 + t = -2.114172784 + 0.46875 t = -2.114172784 + 0.46875 Combine like terms: -2.114172784 + 0.46875 = -1.645422784 t = -1.645422784 Simplifying t = -1.645422784Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.582922784, -1.645422784}
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