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Simplifying t = -4.9t2 + 4t + 10 Reorder the terms: t = 10 + 4t + -4.9t2 Solving t = 10 + 4t + -4.9t2 Solving for variable 't'. Reorder the terms: -10 + t + -4t + 4.9t2 = 10 + 4t + -4.9t2 + -10 + -4t + 4.9t2 Combine like terms: t + -4t = -3t -10 + -3t + 4.9t2 = 10 + 4t + -4.9t2 + -10 + -4t + 4.9t2 Reorder the terms: -10 + -3t + 4.9t2 = 10 + -10 + 4t + -4t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + -3t + 4.9t2 = 0 + 4t + -4t + -4.9t2 + 4.9t2 -10 + -3t + 4.9t2 = 4t + -4t + -4.9t2 + 4.9t2 Combine like terms: 4t + -4t = 0 -10 + -3t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -10 + -3t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -3t + 4.9t2 = 0.0 Begin completing the square. Divide all terms by 4.9 the coefficient of the squared term: Divide each side by '4.9'. -2.040816327 + -0.612244898t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -0.612244898t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -0.612244898t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -0.612244898t + t2 = 0 + 2.040816327 -0.612244898t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -0.612244898t + t2 = 2.040816327 The t term is -0.612244898t. Take half its coefficient (-0.306122449). Square it (0.09371095378) and add it to both sides. Add '0.09371095378' to each side of the equation. -0.612244898t + 0.09371095378 + t2 = 2.040816327 + 0.09371095378 Reorder the terms: 0.09371095378 + -0.612244898t + t2 = 2.040816327 + 0.09371095378 Combine like terms: 2.040816327 + 0.09371095378 = 2.13452728078 0.09371095378 + -0.612244898t + t2 = 2.13452728078 Factor a perfect square on the left side: (t + -0.306122449)(t + -0.306122449) = 2.13452728078 Calculate the square root of the right side: 1.461002149 Break this problem into two subproblems by setting (t + -0.306122449) equal to 1.461002149 and -1.461002149.Subproblem 1
t + -0.306122449 = 1.461002149 Simplifying t + -0.306122449 = 1.461002149 Reorder the terms: -0.306122449 + t = 1.461002149 Solving -0.306122449 + t = 1.461002149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + t = 1.461002149 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = 1.461002149 + 0.306122449 t = 1.461002149 + 0.306122449 Combine like terms: 1.461002149 + 0.306122449 = 1.767124598 t = 1.767124598 Simplifying t = 1.767124598Subproblem 2
t + -0.306122449 = -1.461002149 Simplifying t + -0.306122449 = -1.461002149 Reorder the terms: -0.306122449 + t = -1.461002149 Solving -0.306122449 + t = -1.461002149 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.306122449' to each side of the equation. -0.306122449 + 0.306122449 + t = -1.461002149 + 0.306122449 Combine like terms: -0.306122449 + 0.306122449 = 0.000000000 0.000000000 + t = -1.461002149 + 0.306122449 t = -1.461002149 + 0.306122449 Combine like terms: -1.461002149 + 0.306122449 = -1.1548797 t = -1.1548797 Simplifying t = -1.1548797Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.767124598, -1.1548797}
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