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Simplifying 87 = 16t2 + 195t Reorder the terms: 87 = 195t + 16t2 Solving 87 = 195t + 16t2 Solving for variable 't'. Reorder the terms: 87 + -195t + -16t2 = 195t + -195t + 16t2 + -16t2 Combine like terms: 195t + -195t = 0 87 + -195t + -16t2 = 0 + 16t2 + -16t2 87 + -195t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 87 + -195t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -5.4375 + 12.1875t + t2 = 0 Move the constant term to the right: Add '5.4375' to each side of the equation. -5.4375 + 12.1875t + 5.4375 + t2 = 0 + 5.4375 Reorder the terms: -5.4375 + 5.4375 + 12.1875t + t2 = 0 + 5.4375 Combine like terms: -5.4375 + 5.4375 = 0.0000 0.0000 + 12.1875t + t2 = 0 + 5.4375 12.1875t + t2 = 0 + 5.4375 Combine like terms: 0 + 5.4375 = 5.4375 12.1875t + t2 = 5.4375 The t term is 12.1875t. Take half its coefficient (6.09375). Square it (37.13378906) and add it to both sides. Add '37.13378906' to each side of the equation. 12.1875t + 37.13378906 + t2 = 5.4375 + 37.13378906 Reorder the terms: 37.13378906 + 12.1875t + t2 = 5.4375 + 37.13378906 Combine like terms: 5.4375 + 37.13378906 = 42.57128906 37.13378906 + 12.1875t + t2 = 42.57128906 Factor a perfect square on the left side: (t + 6.09375)(t + 6.09375) = 42.57128906 Calculate the square root of the right side: 6.524667736 Break this problem into two subproblems by setting (t + 6.09375) equal to 6.524667736 and -6.524667736.Subproblem 1
t + 6.09375 = 6.524667736 Simplifying t + 6.09375 = 6.524667736 Reorder the terms: 6.09375 + t = 6.524667736 Solving 6.09375 + t = 6.524667736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.09375' to each side of the equation. 6.09375 + -6.09375 + t = 6.524667736 + -6.09375 Combine like terms: 6.09375 + -6.09375 = 0.00000 0.00000 + t = 6.524667736 + -6.09375 t = 6.524667736 + -6.09375 Combine like terms: 6.524667736 + -6.09375 = 0.430917736 t = 0.430917736 Simplifying t = 0.430917736Subproblem 2
t + 6.09375 = -6.524667736 Simplifying t + 6.09375 = -6.524667736 Reorder the terms: 6.09375 + t = -6.524667736 Solving 6.09375 + t = -6.524667736 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6.09375' to each side of the equation. 6.09375 + -6.09375 + t = -6.524667736 + -6.09375 Combine like terms: 6.09375 + -6.09375 = 0.00000 0.00000 + t = -6.524667736 + -6.09375 t = -6.524667736 + -6.09375 Combine like terms: -6.524667736 + -6.09375 = -12.618417736 t = -12.618417736 Simplifying t = -12.618417736Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.430917736, -12.618417736}
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