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Simplifying 0.0000852t2 + -0.0101t + 0.0613 = 0 Reorder the terms: 0.0613 + -0.0101t + 0.0000852t2 = 0 Solving 0.0613 + -0.0101t + 0.0000852t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 0.0000852 the coefficient of the squared term: Divide each side by '0.0000852'. 719.4835681 + -118.5446009t + t2 = 0 Move the constant term to the right: Add '-719.4835681' to each side of the equation. 719.4835681 + -118.5446009t + -719.4835681 + t2 = 0 + -719.4835681 Reorder the terms: 719.4835681 + -719.4835681 + -118.5446009t + t2 = 0 + -719.4835681 Combine like terms: 719.4835681 + -719.4835681 = 0.0000000 0.0000000 + -118.5446009t + t2 = 0 + -719.4835681 -118.5446009t + t2 = 0 + -719.4835681 Combine like terms: 0 + -719.4835681 = -719.4835681 -118.5446009t + t2 = -719.4835681 The t term is -118.5446009t. Take half its coefficient (-59.27230045). Square it (3513.205601) and add it to both sides. Add '3513.205601' to each side of the equation. -118.5446009t + 3513.205601 + t2 = -719.4835681 + 3513.205601 Reorder the terms: 3513.205601 + -118.5446009t + t2 = -719.4835681 + 3513.205601 Combine like terms: -719.4835681 + 3513.205601 = 2793.7220329 3513.205601 + -118.5446009t + t2 = 2793.7220329 Factor a perfect square on the left side: (t + -59.27230045)(t + -59.27230045) = 2793.7220329 Calculate the square root of the right side: 52.855671719 Break this problem into two subproblems by setting (t + -59.27230045) equal to 52.855671719 and -52.855671719.Subproblem 1
t + -59.27230045 = 52.855671719 Simplifying t + -59.27230045 = 52.855671719 Reorder the terms: -59.27230045 + t = 52.855671719 Solving -59.27230045 + t = 52.855671719 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '59.27230045' to each side of the equation. -59.27230045 + 59.27230045 + t = 52.855671719 + 59.27230045 Combine like terms: -59.27230045 + 59.27230045 = 0.00000000 0.00000000 + t = 52.855671719 + 59.27230045 t = 52.855671719 + 59.27230045 Combine like terms: 52.855671719 + 59.27230045 = 112.127972169 t = 112.127972169 Simplifying t = 112.127972169Subproblem 2
t + -59.27230045 = -52.855671719 Simplifying t + -59.27230045 = -52.855671719 Reorder the terms: -59.27230045 + t = -52.855671719 Solving -59.27230045 + t = -52.855671719 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '59.27230045' to each side of the equation. -59.27230045 + 59.27230045 + t = -52.855671719 + 59.27230045 Combine like terms: -59.27230045 + 59.27230045 = 0.00000000 0.00000000 + t = -52.855671719 + 59.27230045 t = -52.855671719 + 59.27230045 Combine like terms: -52.855671719 + 59.27230045 = 6.416628731 t = 6.416628731 Simplifying t = 6.416628731Solution
The solution to the problem is based on the solutions from the subproblems. t = {112.127972169, 6.416628731}
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