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Simplifying 10 = -4.9t2 + 1.5t + 17 Reorder the terms: 10 = 17 + 1.5t + -4.9t2 Solving 10 = 17 + 1.5t + -4.9t2 Solving for variable 't'. Combine like terms: 10 + -17 = -7 -7 + -1.5t + 4.9t2 = 17 + 1.5t + -4.9t2 + -17 + -1.5t + 4.9t2 Reorder the terms: -7 + -1.5t + 4.9t2 = 17 + -17 + 1.5t + -1.5t + -4.9t2 + 4.9t2 Combine like terms: 17 + -17 = 0 -7 + -1.5t + 4.9t2 = 0 + 1.5t + -1.5t + -4.9t2 + 4.9t2 -7 + -1.5t + 4.9t2 = 1.5t + -1.5t + -4.9t2 + 4.9t2 Combine like terms: 1.5t + -1.5t = 0.0 -7 + -1.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -7 + -1.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -7 + -1.5t + 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'. -1.428571429 + -0.306122449t + t2 = 0 Move the constant term to the right: Add '1.428571429' to each side of the equation. -1.428571429 + -0.306122449t + 1.428571429 + t2 = 0 + 1.428571429 Reorder the terms: -1.428571429 + 1.428571429 + -0.306122449t + t2 = 0 + 1.428571429 Combine like terms: -1.428571429 + 1.428571429 = 0.000000000 0.000000000 + -0.306122449t + t2 = 0 + 1.428571429 -0.306122449t + t2 = 0 + 1.428571429 Combine like terms: 0 + 1.428571429 = 1.428571429 -0.306122449t + t2 = 1.428571429 The t term is -0.306122449t. Take half its coefficient (-0.1530612245). Square it (0.02342773845) and add it to both sides. Add '0.02342773845' to each side of the equation. -0.306122449t + 0.02342773845 + t2 = 1.428571429 + 0.02342773845 Reorder the terms: 0.02342773845 + -0.306122449t + t2 = 1.428571429 + 0.02342773845 Combine like terms: 1.428571429 + 0.02342773845 = 1.45199916745 0.02342773845 + -0.306122449t + t2 = 1.45199916745 Factor a perfect square on the left side: (t + -0.1530612245)(t + -0.1530612245) = 1.45199916745 Calculate the square root of the right side: 1.204989281 Break this problem into two subproblems by setting (t + -0.1530612245) equal to 1.204989281 and -1.204989281.Subproblem 1
t + -0.1530612245 = 1.204989281 Simplifying t + -0.1530612245 = 1.204989281 Reorder the terms: -0.1530612245 + t = 1.204989281 Solving -0.1530612245 + t = 1.204989281 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + t = 1.204989281 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = 1.204989281 + 0.1530612245 t = 1.204989281 + 0.1530612245 Combine like terms: 1.204989281 + 0.1530612245 = 1.3580505055 t = 1.3580505055 Simplifying t = 1.3580505055Subproblem 2
t + -0.1530612245 = -1.204989281 Simplifying t + -0.1530612245 = -1.204989281 Reorder the terms: -0.1530612245 + t = -1.204989281 Solving -0.1530612245 + t = -1.204989281 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.1530612245' to each side of the equation. -0.1530612245 + 0.1530612245 + t = -1.204989281 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = -1.204989281 + 0.1530612245 t = -1.204989281 + 0.1530612245 Combine like terms: -1.204989281 + 0.1530612245 = -1.0519280565 t = -1.0519280565 Simplifying t = -1.0519280565Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.3580505055, -1.0519280565}
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