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Simplifying -16t2 + 76t + 6.3 = 0 Reorder the terms: 6.3 + 76t + -16t2 = 0 Solving 6.3 + 76t + -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'. -0.39375 + -4.75t + t2 = 0 Move the constant term to the right: Add '0.39375' to each side of the equation. -0.39375 + -4.75t + 0.39375 + t2 = 0 + 0.39375 Reorder the terms: -0.39375 + 0.39375 + -4.75t + t2 = 0 + 0.39375 Combine like terms: -0.39375 + 0.39375 = 0.00000 0.00000 + -4.75t + t2 = 0 + 0.39375 -4.75t + t2 = 0 + 0.39375 Combine like terms: 0 + 0.39375 = 0.39375 -4.75t + t2 = 0.39375 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 = 0.39375 + 5.640625 Reorder the terms: 5.640625 + -4.75t + t2 = 0.39375 + 5.640625 Combine like terms: 0.39375 + 5.640625 = 6.034375 5.640625 + -4.75t + t2 = 6.034375 Factor a perfect square on the left side: (t + -2.375)(t + -2.375) = 6.034375 Calculate the square root of the right side: 2.456496489 Break this problem into two subproblems by setting (t + -2.375) equal to 2.456496489 and -2.456496489.Subproblem 1
t + -2.375 = 2.456496489 Simplifying t + -2.375 = 2.456496489 Reorder the terms: -2.375 + t = 2.456496489 Solving -2.375 + t = 2.456496489 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 = 2.456496489 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + t = 2.456496489 + 2.375 t = 2.456496489 + 2.375 Combine like terms: 2.456496489 + 2.375 = 4.831496489 t = 4.831496489 Simplifying t = 4.831496489Subproblem 2
t + -2.375 = -2.456496489 Simplifying t + -2.375 = -2.456496489 Reorder the terms: -2.375 + t = -2.456496489 Solving -2.375 + t = -2.456496489 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 = -2.456496489 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + t = -2.456496489 + 2.375 t = -2.456496489 + 2.375 Combine like terms: -2.456496489 + 2.375 = -0.081496489 t = -0.081496489 Simplifying t = -0.081496489Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.831496489, -0.081496489}
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