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Simplifying 0 = 4t2 + -3t + -70 Reorder the terms: 0 = -70 + -3t + 4t2 Solving 0 = -70 + -3t + 4t2 Solving for variable 't'. Combine like terms: 0 + 70 = 70 70 + 3t + -4t2 = -70 + -3t + 4t2 + 70 + 3t + -4t2 Reorder the terms: 70 + 3t + -4t2 = -70 + 70 + -3t + 3t + 4t2 + -4t2 Combine like terms: -70 + 70 = 0 70 + 3t + -4t2 = 0 + -3t + 3t + 4t2 + -4t2 70 + 3t + -4t2 = -3t + 3t + 4t2 + -4t2 Combine like terms: -3t + 3t = 0 70 + 3t + -4t2 = 0 + 4t2 + -4t2 70 + 3t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 70 + 3t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -17.5 + -0.75t + t2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + -0.75t + 17.5 + t2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + -0.75t + t2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + -0.75t + t2 = 0 + 17.5 -0.75t + t2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 -0.75t + t2 = 17.5 The t term is -0.75t. Take half its coefficient (-0.375). Square it (0.140625) and add it to both sides. Add '0.140625' to each side of the equation. -0.75t + 0.140625 + t2 = 17.5 + 0.140625 Reorder the terms: 0.140625 + -0.75t + t2 = 17.5 + 0.140625 Combine like terms: 17.5 + 0.140625 = 17.640625 0.140625 + -0.75t + t2 = 17.640625 Factor a perfect square on the left side: (t + -0.375)(t + -0.375) = 17.640625 Calculate the square root of the right side: 4.200074404 Break this problem into two subproblems by setting (t + -0.375) equal to 4.200074404 and -4.200074404.Subproblem 1
t + -0.375 = 4.200074404 Simplifying t + -0.375 = 4.200074404 Reorder the terms: -0.375 + t = 4.200074404 Solving -0.375 + t = 4.200074404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = 4.200074404 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = 4.200074404 + 0.375 t = 4.200074404 + 0.375 Combine like terms: 4.200074404 + 0.375 = 4.575074404 t = 4.575074404 Simplifying t = 4.575074404Subproblem 2
t + -0.375 = -4.200074404 Simplifying t + -0.375 = -4.200074404 Reorder the terms: -0.375 + t = -4.200074404 Solving -0.375 + t = -4.200074404 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.375' to each side of the equation. -0.375 + 0.375 + t = -4.200074404 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + t = -4.200074404 + 0.375 t = -4.200074404 + 0.375 Combine like terms: -4.200074404 + 0.375 = -3.825074404 t = -3.825074404 Simplifying t = -3.825074404Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.575074404, -3.825074404}
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