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Simplifying t = -16t2 + 70t + 9 Reorder the terms: t = 9 + 70t + -16t2 Solving t = 9 + 70t + -16t2 Solving for variable 't'. Reorder the terms: -9 + t + -70t + 16t2 = 9 + 70t + -16t2 + -9 + -70t + 16t2 Combine like terms: t + -70t = -69t -9 + -69t + 16t2 = 9 + 70t + -16t2 + -9 + -70t + 16t2 Reorder the terms: -9 + -69t + 16t2 = 9 + -9 + 70t + -70t + -16t2 + 16t2 Combine like terms: 9 + -9 = 0 -9 + -69t + 16t2 = 0 + 70t + -70t + -16t2 + 16t2 -9 + -69t + 16t2 = 70t + -70t + -16t2 + 16t2 Combine like terms: 70t + -70t = 0 -9 + -69t + 16t2 = 0 + -16t2 + 16t2 -9 + -69t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -9 + -69t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.5625 + -4.3125t + t2 = 0 Move the constant term to the right: Add '0.5625' to each side of the equation. -0.5625 + -4.3125t + 0.5625 + t2 = 0 + 0.5625 Reorder the terms: -0.5625 + 0.5625 + -4.3125t + t2 = 0 + 0.5625 Combine like terms: -0.5625 + 0.5625 = 0.0000 0.0000 + -4.3125t + t2 = 0 + 0.5625 -4.3125t + t2 = 0 + 0.5625 Combine like terms: 0 + 0.5625 = 0.5625 -4.3125t + t2 = 0.5625 The t term is -4.3125t. Take half its coefficient (-2.15625). Square it (4.649414063) and add it to both sides. Add '4.649414063' to each side of the equation. -4.3125t + 4.649414063 + t2 = 0.5625 + 4.649414063 Reorder the terms: 4.649414063 + -4.3125t + t2 = 0.5625 + 4.649414063 Combine like terms: 0.5625 + 4.649414063 = 5.211914063 4.649414063 + -4.3125t + t2 = 5.211914063 Factor a perfect square on the left side: (t + -2.15625)(t + -2.15625) = 5.211914063 Calculate the square root of the right side: 2.282961687 Break this problem into two subproblems by setting (t + -2.15625) equal to 2.282961687 and -2.282961687.Subproblem 1
t + -2.15625 = 2.282961687 Simplifying t + -2.15625 = 2.282961687 Reorder the terms: -2.15625 + t = 2.282961687 Solving -2.15625 + t = 2.282961687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + t = 2.282961687 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + t = 2.282961687 + 2.15625 t = 2.282961687 + 2.15625 Combine like terms: 2.282961687 + 2.15625 = 4.439211687 t = 4.439211687 Simplifying t = 4.439211687Subproblem 2
t + -2.15625 = -2.282961687 Simplifying t + -2.15625 = -2.282961687 Reorder the terms: -2.15625 + t = -2.282961687 Solving -2.15625 + t = -2.282961687 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2.15625' to each side of the equation. -2.15625 + 2.15625 + t = -2.282961687 + 2.15625 Combine like terms: -2.15625 + 2.15625 = 0.00000 0.00000 + t = -2.282961687 + 2.15625 t = -2.282961687 + 2.15625 Combine like terms: -2.282961687 + 2.15625 = -0.126711687 t = -0.126711687 Simplifying t = -0.126711687Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.439211687, -0.126711687}
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