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Simplifying -16t2 + 2.2t + 3.5 = 0 Reorder the terms: 3.5 + 2.2t + -16t2 = 0 Solving 3.5 + 2.2t + -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'. -0.21875 + -0.1375t + t2 = 0 Move the constant term to the right: Add '0.21875' to each side of the equation. -0.21875 + -0.1375t + 0.21875 + t2 = 0 + 0.21875 Reorder the terms: -0.21875 + 0.21875 + -0.1375t + t2 = 0 + 0.21875 Combine like terms: -0.21875 + 0.21875 = 0.00000 0.00000 + -0.1375t + t2 = 0 + 0.21875 -0.1375t + t2 = 0 + 0.21875 Combine like terms: 0 + 0.21875 = 0.21875 -0.1375t + t2 = 0.21875 The t term is -0.1375t. Take half its coefficient (-0.06875). Square it (0.0047265625) and add it to both sides. Add '0.0047265625' to each side of the equation. -0.1375t + 0.0047265625 + t2 = 0.21875 + 0.0047265625 Reorder the terms: 0.0047265625 + -0.1375t + t2 = 0.21875 + 0.0047265625 Combine like terms: 0.21875 + 0.0047265625 = 0.2234765625 0.0047265625 + -0.1375t + t2 = 0.2234765625 Factor a perfect square on the left side: (t + -0.06875)(t + -0.06875) = 0.2234765625 Calculate the square root of the right side: 0.472733077 Break this problem into two subproblems by setting (t + -0.06875) equal to 0.472733077 and -0.472733077.Subproblem 1
t + -0.06875 = 0.472733077 Simplifying t + -0.06875 = 0.472733077 Reorder the terms: -0.06875 + t = 0.472733077 Solving -0.06875 + t = 0.472733077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06875' to each side of the equation. -0.06875 + 0.06875 + t = 0.472733077 + 0.06875 Combine like terms: -0.06875 + 0.06875 = 0.00000 0.00000 + t = 0.472733077 + 0.06875 t = 0.472733077 + 0.06875 Combine like terms: 0.472733077 + 0.06875 = 0.541483077 t = 0.541483077 Simplifying t = 0.541483077Subproblem 2
t + -0.06875 = -0.472733077 Simplifying t + -0.06875 = -0.472733077 Reorder the terms: -0.06875 + t = -0.472733077 Solving -0.06875 + t = -0.472733077 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.06875' to each side of the equation. -0.06875 + 0.06875 + t = -0.472733077 + 0.06875 Combine like terms: -0.06875 + 0.06875 = 0.00000 0.00000 + t = -0.472733077 + 0.06875 t = -0.472733077 + 0.06875 Combine like terms: -0.472733077 + 0.06875 = -0.403983077 t = -0.403983077 Simplifying t = -0.403983077Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.541483077, -0.403983077}
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