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Simplifying 235t + -16t2 + 151 = 0 Reorder the terms: 151 + 235t + -16t2 = 0 Solving 151 + 235t + -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'. -9.4375 + -14.6875t + t2 = 0 Move the constant term to the right: Add '9.4375' to each side of the equation. -9.4375 + -14.6875t + 9.4375 + t2 = 0 + 9.4375 Reorder the terms: -9.4375 + 9.4375 + -14.6875t + t2 = 0 + 9.4375 Combine like terms: -9.4375 + 9.4375 = 0.0000 0.0000 + -14.6875t + t2 = 0 + 9.4375 -14.6875t + t2 = 0 + 9.4375 Combine like terms: 0 + 9.4375 = 9.4375 -14.6875t + t2 = 9.4375 The t term is -14.6875t. Take half its coefficient (-7.34375). Square it (53.93066406) and add it to both sides. Add '53.93066406' to each side of the equation. -14.6875t + 53.93066406 + t2 = 9.4375 + 53.93066406 Reorder the terms: 53.93066406 + -14.6875t + t2 = 9.4375 + 53.93066406 Combine like terms: 9.4375 + 53.93066406 = 63.36816406 53.93066406 + -14.6875t + t2 = 63.36816406 Factor a perfect square on the left side: (t + -7.34375)(t + -7.34375) = 63.36816406 Calculate the square root of the right side: 7.960412305 Break this problem into two subproblems by setting (t + -7.34375) equal to 7.960412305 and -7.960412305.Subproblem 1
t + -7.34375 = 7.960412305 Simplifying t + -7.34375 = 7.960412305 Reorder the terms: -7.34375 + t = 7.960412305 Solving -7.34375 + t = 7.960412305 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.34375' to each side of the equation. -7.34375 + 7.34375 + t = 7.960412305 + 7.34375 Combine like terms: -7.34375 + 7.34375 = 0.00000 0.00000 + t = 7.960412305 + 7.34375 t = 7.960412305 + 7.34375 Combine like terms: 7.960412305 + 7.34375 = 15.304162305 t = 15.304162305 Simplifying t = 15.304162305Subproblem 2
t + -7.34375 = -7.960412305 Simplifying t + -7.34375 = -7.960412305 Reorder the terms: -7.34375 + t = -7.960412305 Solving -7.34375 + t = -7.960412305 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.34375' to each side of the equation. -7.34375 + 7.34375 + t = -7.960412305 + 7.34375 Combine like terms: -7.34375 + 7.34375 = 0.00000 0.00000 + t = -7.960412305 + 7.34375 t = -7.960412305 + 7.34375 Combine like terms: -7.960412305 + 7.34375 = -0.616662305 t = -0.616662305 Simplifying t = -0.616662305Solution
The solution to the problem is based on the solutions from the subproblems. t = {15.304162305, -0.616662305}
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