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Simplifying 50 = 16t2 + 76t + 5 Reorder the terms: 50 = 5 + 76t + 16t2 Solving 50 = 5 + 76t + 16t2 Solving for variable 't'. Combine like terms: 50 + -5 = 45 45 + -76t + -16t2 = 5 + 76t + 16t2 + -5 + -76t + -16t2 Reorder the terms: 45 + -76t + -16t2 = 5 + -5 + 76t + -76t + 16t2 + -16t2 Combine like terms: 5 + -5 = 0 45 + -76t + -16t2 = 0 + 76t + -76t + 16t2 + -16t2 45 + -76t + -16t2 = 76t + -76t + 16t2 + -16t2 Combine like terms: 76t + -76t = 0 45 + -76t + -16t2 = 0 + 16t2 + -16t2 45 + -76t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 45 + -76t + -16t2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -2.8125 + 4.75t + t2 = 0 Move the constant term to the right: Add '2.8125' to each side of the equation. -2.8125 + 4.75t + 2.8125 + t2 = 0 + 2.8125 Reorder the terms: -2.8125 + 2.8125 + 4.75t + t2 = 0 + 2.8125 Combine like terms: -2.8125 + 2.8125 = 0.0000 0.0000 + 4.75t + t2 = 0 + 2.8125 4.75t + t2 = 0 + 2.8125 Combine like terms: 0 + 2.8125 = 2.8125 4.75t + t2 = 2.8125 The t term is 4.75t. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75t + 5.640625 + t2 = 2.8125 + 5.640625 Reorder the terms: 5.640625 + 4.75t + t2 = 2.8125 + 5.640625 Combine like terms: 2.8125 + 5.640625 = 8.453125 5.640625 + 4.75t + t2 = 8.453125 Factor a perfect square on the left side: (t + 2.375)(t + 2.375) = 8.453125 Calculate the square root of the right side: 2.907425837 Break this problem into two subproblems by setting (t + 2.375) equal to 2.907425837 and -2.907425837.Subproblem 1
t + 2.375 = 2.907425837 Simplifying t + 2.375 = 2.907425837 Reorder the terms: 2.375 + t = 2.907425837 Solving 2.375 + t = 2.907425837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = 2.907425837 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = 2.907425837 + -2.375 t = 2.907425837 + -2.375 Combine like terms: 2.907425837 + -2.375 = 0.532425837 t = 0.532425837 Simplifying t = 0.532425837Subproblem 2
t + 2.375 = -2.907425837 Simplifying t + 2.375 = -2.907425837 Reorder the terms: 2.375 + t = -2.907425837 Solving 2.375 + t = -2.907425837 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + t = -2.907425837 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + t = -2.907425837 + -2.375 t = -2.907425837 + -2.375 Combine like terms: -2.907425837 + -2.375 = -5.282425837 t = -5.282425837 Simplifying t = -5.282425837Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.532425837, -5.282425837}
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