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Simplifying 0 = 15 + -10t + -16t2 Solving 0 = 15 + -10t + -16t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + 10t + 16t2 = 15 + -10t + -16t2 + -15 + 10t + 16t2 Reorder the terms: -15 + 10t + 16t2 = 15 + -15 + -10t + 10t + -16t2 + 16t2 Combine like terms: 15 + -15 = 0 -15 + 10t + 16t2 = 0 + -10t + 10t + -16t2 + 16t2 -15 + 10t + 16t2 = -10t + 10t + -16t2 + 16t2 Combine like terms: -10t + 10t = 0 -15 + 10t + 16t2 = 0 + -16t2 + 16t2 -15 + 10t + 16t2 = -16t2 + 16t2 Combine like terms: -16t2 + 16t2 = 0 -15 + 10t + 16t2 = 0 Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. -0.9375 + 0.625t + t2 = 0 Move the constant term to the right: Add '0.9375' to each side of the equation. -0.9375 + 0.625t + 0.9375 + t2 = 0 + 0.9375 Reorder the terms: -0.9375 + 0.9375 + 0.625t + t2 = 0 + 0.9375 Combine like terms: -0.9375 + 0.9375 = 0.0000 0.0000 + 0.625t + t2 = 0 + 0.9375 0.625t + t2 = 0 + 0.9375 Combine like terms: 0 + 0.9375 = 0.9375 0.625t + t2 = 0.9375 The t term is 0.625t. Take half its coefficient (0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. 0.625t + 0.09765625 + t2 = 0.9375 + 0.09765625 Reorder the terms: 0.09765625 + 0.625t + t2 = 0.9375 + 0.09765625 Combine like terms: 0.9375 + 0.09765625 = 1.03515625 0.09765625 + 0.625t + t2 = 1.03515625 Factor a perfect square on the left side: (t + 0.3125)(t + 0.3125) = 1.03515625 Calculate the square root of the right side: 1.017426287 Break this problem into two subproblems by setting (t + 0.3125) equal to 1.017426287 and -1.017426287.Subproblem 1
t + 0.3125 = 1.017426287 Simplifying t + 0.3125 = 1.017426287 Reorder the terms: 0.3125 + t = 1.017426287 Solving 0.3125 + t = 1.017426287 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = 1.017426287 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = 1.017426287 + -0.3125 t = 1.017426287 + -0.3125 Combine like terms: 1.017426287 + -0.3125 = 0.704926287 t = 0.704926287 Simplifying t = 0.704926287Subproblem 2
t + 0.3125 = -1.017426287 Simplifying t + 0.3125 = -1.017426287 Reorder the terms: 0.3125 + t = -1.017426287 Solving 0.3125 + t = -1.017426287 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3125' to each side of the equation. 0.3125 + -0.3125 + t = -1.017426287 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + t = -1.017426287 + -0.3125 t = -1.017426287 + -0.3125 Combine like terms: -1.017426287 + -0.3125 = -1.329926287 t = -1.329926287 Simplifying t = -1.329926287Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.704926287, -1.329926287}
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