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Simplifying (-2.7t2) + 35t + 7 = 10 Reorder the terms: 7 + 35t + (-2.7t2) = 10 Solving 7 + 35t + (-2.7t2) = 10 Solving for variable 't'. Reorder the terms: 7 + -10 + 35t + (-2.7t2) = 10 + -10 Combine like terms: 7 + -10 = -3 -3 + 35t + (-2.7t2) = 10 + -10 Combine like terms: 10 + -10 = 0 -3 + 35t + (-2.7t2) = 0 Begin completing the square. Divide all terms by -2.7 the coefficient of the squared term: Divide each side by '-2.7'. 1.111111111 + -12.96296296t + t2 = 0 Move the constant term to the right: Add '-1.111111111' to each side of the equation. 1.111111111 + -12.96296296t + -1.111111111 + t2 = 0 + -1.111111111 Reorder the terms: 1.111111111 + -1.111111111 + -12.96296296t + t2 = 0 + -1.111111111 Combine like terms: 1.111111111 + -1.111111111 = 0.000000000 0.000000000 + -12.96296296t + t2 = 0 + -1.111111111 -12.96296296t + t2 = 0 + -1.111111111 Combine like terms: 0 + -1.111111111 = -1.111111111 -12.96296296t + t2 = -1.111111111 The t term is -12.96296296t. Take half its coefficient (-6.48148148). Square it (42.00960218) and add it to both sides. Add '42.00960218' to each side of the equation. -12.96296296t + 42.00960218 + t2 = -1.111111111 + 42.00960218 Reorder the terms: 42.00960218 + -12.96296296t + t2 = -1.111111111 + 42.00960218 Combine like terms: -1.111111111 + 42.00960218 = 40.898491069 42.00960218 + -12.96296296t + t2 = 40.898491069 Factor a perfect square on the left side: ((t) + -6.48148148)((t) + -6.48148148) = 40.898491069 Calculate the square root of the right side: 6.395192809 Break this problem into two subproblems by setting ((t) + -6.48148148) equal to 6.395192809 and -6.395192809.Subproblem 1
(t) + -6.48148148 = 6.395192809 Simplifying (t) + -6.48148148 = 6.395192809 t + -6.48148148 = 6.395192809 Reorder the terms: -6.48148148 + t = 6.395192809 Solving -6.48148148 + t = 6.395192809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + t = 6.395192809 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + t = 6.395192809 + 6.48148148 t = 6.395192809 + 6.48148148 Combine like terms: 6.395192809 + 6.48148148 = 12.876674289 t = 12.876674289 Simplifying t = 12.876674289Subproblem 2
(t) + -6.48148148 = -6.395192809 Simplifying (t) + -6.48148148 = -6.395192809 t + -6.48148148 = -6.395192809 Reorder the terms: -6.48148148 + t = -6.395192809 Solving -6.48148148 + t = -6.395192809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6.48148148' to each side of the equation. -6.48148148 + 6.48148148 + t = -6.395192809 + 6.48148148 Combine like terms: -6.48148148 + 6.48148148 = 0.00000000 0.00000000 + t = -6.395192809 + 6.48148148 t = -6.395192809 + 6.48148148 Combine like terms: -6.395192809 + 6.48148148 = 0.086288671 t = 0.086288671 Simplifying t = 0.086288671Solution
The solution to the problem is based on the solutions from the subproblems. t = {12.876674289, 0.086288671}
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