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Simplifying 0.0915t2 + -0.934t = 1.763 Reorder the terms: -0.934t + 0.0915t2 = 1.763 Solving -0.934t + 0.0915t2 = 1.763 Solving for variable 't'. Reorder the terms: -1.763 + -0.934t + 0.0915t2 = 1.763 + -1.763 Combine like terms: 1.763 + -1.763 = 0.000 -1.763 + -0.934t + 0.0915t2 = 0.000 Begin completing the square. Divide all terms by 0.0915 the coefficient of the squared term: Divide each side by '0.0915'. -19.26775956 + -10.20765027t + t2 = 0 Move the constant term to the right: Add '19.26775956' to each side of the equation. -19.26775956 + -10.20765027t + 19.26775956 + t2 = 0 + 19.26775956 Reorder the terms: -19.26775956 + 19.26775956 + -10.20765027t + t2 = 0 + 19.26775956 Combine like terms: -19.26775956 + 19.26775956 = 0.00000000 0.00000000 + -10.20765027t + t2 = 0 + 19.26775956 -10.20765027t + t2 = 0 + 19.26775956 Combine like terms: 0 + 19.26775956 = 19.26775956 -10.20765027t + t2 = 19.26775956 The t term is -10.20765027t. Take half its coefficient (-5.103825135). Square it (26.04903101) and add it to both sides. Add '26.04903101' to each side of the equation. -10.20765027t + 26.04903101 + t2 = 19.26775956 + 26.04903101 Reorder the terms: 26.04903101 + -10.20765027t + t2 = 19.26775956 + 26.04903101 Combine like terms: 19.26775956 + 26.04903101 = 45.31679057 26.04903101 + -10.20765027t + t2 = 45.31679057 Factor a perfect square on the left side: (t + -5.103825135)(t + -5.103825135) = 45.31679057 Calculate the square root of the right side: 6.731774697 Break this problem into two subproblems by setting (t + -5.103825135) equal to 6.731774697 and -6.731774697.Subproblem 1
t + -5.103825135 = 6.731774697 Simplifying t + -5.103825135 = 6.731774697 Reorder the terms: -5.103825135 + t = 6.731774697 Solving -5.103825135 + t = 6.731774697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.103825135' to each side of the equation. -5.103825135 + 5.103825135 + t = 6.731774697 + 5.103825135 Combine like terms: -5.103825135 + 5.103825135 = 0.000000000 0.000000000 + t = 6.731774697 + 5.103825135 t = 6.731774697 + 5.103825135 Combine like terms: 6.731774697 + 5.103825135 = 11.835599832 t = 11.835599832 Simplifying t = 11.835599832Subproblem 2
t + -5.103825135 = -6.731774697 Simplifying t + -5.103825135 = -6.731774697 Reorder the terms: -5.103825135 + t = -6.731774697 Solving -5.103825135 + t = -6.731774697 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '5.103825135' to each side of the equation. -5.103825135 + 5.103825135 + t = -6.731774697 + 5.103825135 Combine like terms: -5.103825135 + 5.103825135 = 0.000000000 0.000000000 + t = -6.731774697 + 5.103825135 t = -6.731774697 + 5.103825135 Combine like terms: -6.731774697 + 5.103825135 = -1.627949562 t = -1.627949562 Simplifying t = -1.627949562Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.835599832, -1.627949562}
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