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Simplifying -15 = 64t + -16t2 Solving -15 = 64t + -16t2 Solving for variable 't'. Reorder the terms: -15 + -64t + 16t2 = 64t + -64t + -16t2 + 16t2 Combine like terms: 64t + -64t = 0 -15 + -64t + 16t2 = 0 + -16t2 + 16t2 -15 + -64t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -15 + -64t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + -4t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + -4t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + -4t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + -4t + t2 = 0 + 0.9375 -4t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 -4t + t2 = 0.9375 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 0.9375 + 4 Reorder the terms: 4 + -4t + t2 = 0.9375 + 4 Combine like terms: 0.9375 + 4 = 4.9375 4 + -4t + t2 = 4.9375 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.9375 Calculate the square root of the right side: 2.222048604 Break this problem into two subproblems by setting (t + -2) equal to 2.222048604 and -2.222048604.Subproblem 1
t + -2 = 2.222048604 Simplifying t + -2 = 2.222048604 Reorder the terms: -2 + t = 2.222048604 Solving -2 + t = 2.222048604 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 2.222048604 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.222048604 + 2 t = 2.222048604 + 2 Combine like terms: 2.222048604 + 2 = 4.222048604 t = 4.222048604 Simplifying t = 4.222048604Subproblem 2
t + -2 = -2.222048604 Simplifying t + -2 = -2.222048604 Reorder the terms: -2 + t = -2.222048604 Solving -2 + t = -2.222048604 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -2.222048604 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.222048604 + 2 t = -2.222048604 + 2 Combine like terms: -2.222048604 + 2 = -0.222048604 t = -0.222048604 Simplifying t = -0.222048604Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.222048604, -0.222048604}
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