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Simplifying 212 = -16t2 + 366t Reorder the terms: 212 = 366t + -16t2 Solving 212 = 366t + -16t2 Solving for variable 't'. Reorder the terms: 212 + -366t + 16t2 = 366t + -366t + -16t2 + 16t2 Combine like terms: 366t + -366t = 0 212 + -366t + 16t2 = 0 + -16t2 + 16t2 212 + -366t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 212 + -366t + 16t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(106 + -183t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(106 + -183t + 8t2)' equal to zero and attempt to solve: Simplifying 106 + -183t + 8t2 = 0 Solving 106 + -183t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 13.25 + -22.875t + t2 = 0 Move the constant term to the right: Add '-13.25' to each side of the equation. 13.25 + -22.875t + -13.25 + t2 = 0 + -13.25 Reorder the terms: 13.25 + -13.25 + -22.875t + t2 = 0 + -13.25 Combine like terms: 13.25 + -13.25 = 0.00 0.00 + -22.875t + t2 = 0 + -13.25 -22.875t + t2 = 0 + -13.25 Combine like terms: 0 + -13.25 = -13.25 -22.875t + t2 = -13.25 The t term is -22.875t. Take half its coefficient (-11.4375). Square it (130.8164063) and add it to both sides. Add '130.8164063' to each side of the equation. -22.875t + 130.8164063 + t2 = -13.25 + 130.8164063 Reorder the terms: 130.8164063 + -22.875t + t2 = -13.25 + 130.8164063 Combine like terms: -13.25 + 130.8164063 = 117.5664063 130.8164063 + -22.875t + t2 = 117.5664063 Factor a perfect square on the left side: (t + -11.4375)(t + -11.4375) = 117.5664063 Calculate the square root of the right side: 10.842804356 Break this problem into two subproblems by setting (t + -11.4375) equal to 10.842804356 and -10.842804356.Subproblem 1
t + -11.4375 = 10.842804356 Simplifying t + -11.4375 = 10.842804356 Reorder the terms: -11.4375 + t = 10.842804356 Solving -11.4375 + t = 10.842804356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.4375' to each side of the equation. -11.4375 + 11.4375 + t = 10.842804356 + 11.4375 Combine like terms: -11.4375 + 11.4375 = 0.0000 0.0000 + t = 10.842804356 + 11.4375 t = 10.842804356 + 11.4375 Combine like terms: 10.842804356 + 11.4375 = 22.280304356 t = 22.280304356 Simplifying t = 22.280304356Subproblem 2
t + -11.4375 = -10.842804356 Simplifying t + -11.4375 = -10.842804356 Reorder the terms: -11.4375 + t = -10.842804356 Solving -11.4375 + t = -10.842804356 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '11.4375' to each side of the equation. -11.4375 + 11.4375 + t = -10.842804356 + 11.4375 Combine like terms: -11.4375 + 11.4375 = 0.0000 0.0000 + t = -10.842804356 + 11.4375 t = -10.842804356 + 11.4375 Combine like terms: -10.842804356 + 11.4375 = 0.594695644 t = 0.594695644 Simplifying t = 0.594695644Solution
The solution to the problem is based on the solutions from the subproblems. t = {22.280304356, 0.594695644}Solution
t = {22.280304356, 0.594695644}
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