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Simplifying 0.0915t2 + -0.934t + 1.763 = 0 Reorder the terms: 1.763 + -0.934t + 0.0915t2 = 0 Solving 1.763 + -0.934t + 0.0915t2 = 0 Solving for variable 't'. 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 = 6.78127145 26.04903101 + -10.20765027t + t2 = 6.78127145 Factor a perfect square on the left side: (t + -5.103825135)(t + -5.103825135) = 6.78127145 Calculate the square root of the right side: 2.604087451 Break this problem into two subproblems by setting (t + -5.103825135) equal to 2.604087451 and -2.604087451.Subproblem 1
t + -5.103825135 = 2.604087451 Simplifying t + -5.103825135 = 2.604087451 Reorder the terms: -5.103825135 + t = 2.604087451 Solving -5.103825135 + t = 2.604087451 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 = 2.604087451 + 5.103825135 Combine like terms: -5.103825135 + 5.103825135 = 0.000000000 0.000000000 + t = 2.604087451 + 5.103825135 t = 2.604087451 + 5.103825135 Combine like terms: 2.604087451 + 5.103825135 = 7.707912586 t = 7.707912586 Simplifying t = 7.707912586Subproblem 2
t + -5.103825135 = -2.604087451 Simplifying t + -5.103825135 = -2.604087451 Reorder the terms: -5.103825135 + t = -2.604087451 Solving -5.103825135 + t = -2.604087451 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 = -2.604087451 + 5.103825135 Combine like terms: -5.103825135 + 5.103825135 = 0.000000000 0.000000000 + t = -2.604087451 + 5.103825135 t = -2.604087451 + 5.103825135 Combine like terms: -2.604087451 + 5.103825135 = 2.499737684 t = 2.499737684 Simplifying t = 2.499737684Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.707912586, 2.499737684}
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