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Simplifying 0 = -4.9t2 + 1.5t + 12 Reorder the terms: 0 = 12 + 1.5t + -4.9t2 Solving 0 = 12 + 1.5t + -4.9t2 Solving for variable 't'. Combine like terms: 0 + -12 = -12 -12 + -1.5t + 4.9t2 = 12 + 1.5t + -4.9t2 + -12 + -1.5t + 4.9t2 Reorder the terms: -12 + -1.5t + 4.9t2 = 12 + -12 + 1.5t + -1.5t + -4.9t2 + 4.9t2 Combine like terms: 12 + -12 = 0 -12 + -1.5t + 4.9t2 = 0 + 1.5t + -1.5t + -4.9t2 + 4.9t2 -12 + -1.5t + 4.9t2 = 1.5t + -1.5t + -4.9t2 + 4.9t2 Combine like terms: 1.5t + -1.5t = 0.0 -12 + -1.5t + 4.9t2 = 0.0 + -4.9t2 + 4.9t2 -12 + -1.5t + 4.9t2 = -4.9t2 + 4.9t2 Combine like terms: -4.9t2 + 4.9t2 = 0.0 -12 + -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'. -2.448979592 + -0.306122449t + t2 = 0 Move the constant term to the right: Add '2.448979592' to each side of the equation. -2.448979592 + -0.306122449t + 2.448979592 + t2 = 0 + 2.448979592 Reorder the terms: -2.448979592 + 2.448979592 + -0.306122449t + t2 = 0 + 2.448979592 Combine like terms: -2.448979592 + 2.448979592 = 0.000000000 0.000000000 + -0.306122449t + t2 = 0 + 2.448979592 -0.306122449t + t2 = 0 + 2.448979592 Combine like terms: 0 + 2.448979592 = 2.448979592 -0.306122449t + t2 = 2.448979592 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 = 2.448979592 + 0.02342773845 Reorder the terms: 0.02342773845 + -0.306122449t + t2 = 2.448979592 + 0.02342773845 Combine like terms: 2.448979592 + 0.02342773845 = 2.47240733045 0.02342773845 + -0.306122449t + t2 = 2.47240733045 Factor a perfect square on the left side: (t + -0.1530612245)(t + -0.1530612245) = 2.47240733045 Calculate the square root of the right side: 1.572389052 Break this problem into two subproblems by setting (t + -0.1530612245) equal to 1.572389052 and -1.572389052.Subproblem 1
t + -0.1530612245 = 1.572389052 Simplifying t + -0.1530612245 = 1.572389052 Reorder the terms: -0.1530612245 + t = 1.572389052 Solving -0.1530612245 + t = 1.572389052 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 = 1.572389052 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = 1.572389052 + 0.1530612245 t = 1.572389052 + 0.1530612245 Combine like terms: 1.572389052 + 0.1530612245 = 1.7254502765 t = 1.7254502765 Simplifying t = 1.7254502765Subproblem 2
t + -0.1530612245 = -1.572389052 Simplifying t + -0.1530612245 = -1.572389052 Reorder the terms: -0.1530612245 + t = -1.572389052 Solving -0.1530612245 + t = -1.572389052 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 = -1.572389052 + 0.1530612245 Combine like terms: -0.1530612245 + 0.1530612245 = 0.0000000000 0.0000000000 + t = -1.572389052 + 0.1530612245 t = -1.572389052 + 0.1530612245 Combine like terms: -1.572389052 + 0.1530612245 = -1.4193278275 t = -1.4193278275 Simplifying t = -1.4193278275Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.7254502765, -1.4193278275}
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