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Simplifying 0 = -4.9t2 + 17t + 10 Reorder the terms: 0 = 10 + 17t + -4.9t2 Solving 0 = 10 + 17t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -10 = -10 -10 + -17t + 4.9t2 = 10 + 17t + -4.9t2 + -10 + -17t + 4.9t2 Reorder the terms: -10 + -17t + 4.9t2 = 10 + -10 + 17t + -17t + -4.9t2 + 4.9t2 Combine like terms: 10 + -10 = 0 -10 + -17t + 4.9t2 = 0 + 17t + -17t + -4.9t2 + 4.9t2 -10 + -17t + 4.9t2 = 17t + -17t + -4.9t2 + 4.9t2 Combine like terms: 17t + -17t = 0 -10 + -17t + 4.9t2 = 0 + -4.9t2 + 4.9t2 -10 + -17t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -10 + -17t + 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 + -3.469387755t + t2 = 0 Move the constant term to the right: Add '2.040816327' to each side of the equation. -2.040816327 + -3.469387755t + 2.040816327 + t2 = 0 + 2.040816327 Reorder the terms: -2.040816327 + 2.040816327 + -3.469387755t + t2 = 0 + 2.040816327 Combine like terms: -2.040816327 + 2.040816327 = 0.000000000 0.000000000 + -3.469387755t + t2 = 0 + 2.040816327 -3.469387755t + t2 = 0 + 2.040816327 Combine like terms: 0 + 2.040816327 = 2.040816327 -3.469387755t + t2 = 2.040816327 The t term is -3.469387755t. Take half its coefficient (-1.734693878). Square it (3.009162850) and add it to both sides. Add '3.009162850' to each side of the equation. -3.469387755t + 3.009162850 + t2 = 2.040816327 + 3.009162850 Reorder the terms: 3.009162850 + -3.469387755t + t2 = 2.040816327 + 3.009162850 Combine like terms: 2.040816327 + 3.009162850 = 5.049979177 3.009162850 + -3.469387755t + t2 = 5.049979177 Factor a perfect square on the left side: (t + -1.734693878)(t + -1.734693878) = 5.049979177 Calculate the square root of the right side: 2.247215872 Break this problem into two subproblems by setting (t + -1.734693878) equal to 2.247215872 and -2.247215872.Subproblem 1
t + -1.734693878 = 2.247215872 Simplifying t + -1.734693878 = 2.247215872 Reorder the terms: -1.734693878 + t = 2.247215872 Solving -1.734693878 + t = 2.247215872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + t = 2.247215872 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + t = 2.247215872 + 1.734693878 t = 2.247215872 + 1.734693878 Combine like terms: 2.247215872 + 1.734693878 = 3.98190975 t = 3.98190975 Simplifying t = 3.98190975Subproblem 2
t + -1.734693878 = -2.247215872 Simplifying t + -1.734693878 = -2.247215872 Reorder the terms: -1.734693878 + t = -2.247215872 Solving -1.734693878 + t = -2.247215872 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.734693878' to each side of the equation. -1.734693878 + 1.734693878 + t = -2.247215872 + 1.734693878 Combine like terms: -1.734693878 + 1.734693878 = 0.000000000 0.000000000 + t = -2.247215872 + 1.734693878 t = -2.247215872 + 1.734693878 Combine like terms: -2.247215872 + 1.734693878 = -0.512521994 t = -0.512521994 Simplifying t = -0.512521994Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.98190975, -0.512521994}
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