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Simplifying 0 = -16t2 + 75t + 100 Reorder the terms: 0 = 100 + 75t + -16t2 Solving 0 = 100 + 75t + -16t2 Solving for variable 't'. Combine like terms: 0 + -100 = -100 -100 + -75t + 16t2 = 100 + 75t + -16t2 + -100 + -75t + 16t2 Reorder the terms: -100 + -75t + 16t2 = 100 + -100 + 75t + -75t + -16t2 + 16t2 Combine like terms: 100 + -100 = 0 -100 + -75t + 16t2 = 0 + 75t + -75t + -16t2 + 16t2 -100 + -75t + 16t2 = 75t + -75t + -16t2 + 16t2 Combine like terms: 75t + -75t = 0 -100 + -75t + 16t2 = 0 + -16t2 + 16t2 -100 + -75t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -100 + -75t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -6.25 + -4.6875t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -4.6875t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -4.6875t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -4.6875t + t2 = 0 + 6.25 -4.6875t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -4.6875t + t2 = 6.25 The t term is -4.6875t. Take half its coefficient (-2.34375). Square it (5.493164063) and add it to both sides. Add '5.493164063' to each side of the equation. -4.6875t + 5.493164063 + t2 = 6.25 + 5.493164063 Reorder the terms: 5.493164063 + -4.6875t + t2 = 6.25 + 5.493164063 Combine like terms: 6.25 + 5.493164063 = 11.743164063 5.493164063 + -4.6875t + t2 = 11.743164063 Factor a perfect square on the left side: (t + -2.34375)(t + -2.34375) = 11.743164063 Calculate the square root of the right side: 3.426830031 Break this problem into two subproblems by setting (t + -2.34375) equal to 3.426830031 and -3.426830031.Subproblem 1
t + -2.34375 = 3.426830031 Simplifying t + -2.34375 = 3.426830031 Reorder the terms: -2.34375 + t = 3.426830031 Solving -2.34375 + t = 3.426830031 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = 3.426830031 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = 3.426830031 + 2.34375 t = 3.426830031 + 2.34375 Combine like terms: 3.426830031 + 2.34375 = 5.770580031 t = 5.770580031 Simplifying t = 5.770580031Subproblem 2
t + -2.34375 = -3.426830031 Simplifying t + -2.34375 = -3.426830031 Reorder the terms: -2.34375 + t = -3.426830031 Solving -2.34375 + t = -3.426830031 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.34375' to each side of the equation. -2.34375 + 2.34375 + t = -3.426830031 + 2.34375 Combine like terms: -2.34375 + 2.34375 = 0.00000 0.00000 + t = -3.426830031 + 2.34375 t = -3.426830031 + 2.34375 Combine like terms: -3.426830031 + 2.34375 = -1.083080031 t = -1.083080031 Simplifying t = -1.083080031Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.770580031, -1.083080031}
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