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Simplifying -4.9(t2 + 32t) + 2 = 0 Reorder the terms: -4.9(32t + t2) + 2 = 0 (32t * -4.9 + t2 * -4.9) + 2 = 0 (-156.8t + -4.9t2) + 2 = 0 Reorder the terms: 2 + -156.8t + -4.9t2 = 0 Solving 2 + -156.8t + -4.9t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -4.9 the coefficient of the squared term: Divide each side by '-4.9'. -0.4081632653 + 32t + t2 = 0 Move the constant term to the right: Add '0.4081632653' to each side of the equation. -0.4081632653 + 32t + 0.4081632653 + t2 = 0 + 0.4081632653 Reorder the terms: -0.4081632653 + 0.4081632653 + 32t + t2 = 0 + 0.4081632653 Combine like terms: -0.4081632653 + 0.4081632653 = 0.0000000000 0.0000000000 + 32t + t2 = 0 + 0.4081632653 32t + t2 = 0 + 0.4081632653 Combine like terms: 0 + 0.4081632653 = 0.4081632653 32t + t2 = 0.4081632653 The t term is 32t. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32t + 256 + t2 = 0.4081632653 + 256 Reorder the terms: 256 + 32t + t2 = 0.4081632653 + 256 Combine like terms: 0.4081632653 + 256 = 256.4081632653 256 + 32t + t2 = 256.4081632653 Factor a perfect square on the left side: (t + 16)(t + 16) = 256.4081632653 Calculate the square root of the right side: 16.012750022 Break this problem into two subproblems by setting (t + 16) equal to 16.012750022 and -16.012750022.Subproblem 1
t + 16 = 16.012750022 Simplifying t + 16 = 16.012750022 Reorder the terms: 16 + t = 16.012750022 Solving 16 + t = 16.012750022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + t = 16.012750022 + -16 Combine like terms: 16 + -16 = 0 0 + t = 16.012750022 + -16 t = 16.012750022 + -16 Combine like terms: 16.012750022 + -16 = 0.012750022 t = 0.012750022 Simplifying t = 0.012750022Subproblem 2
t + 16 = -16.012750022 Simplifying t + 16 = -16.012750022 Reorder the terms: 16 + t = -16.012750022 Solving 16 + t = -16.012750022 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + t = -16.012750022 + -16 Combine like terms: 16 + -16 = 0 0 + t = -16.012750022 + -16 t = -16.012750022 + -16 Combine like terms: -16.012750022 + -16 = -32.012750022 t = -32.012750022 Simplifying t = -32.012750022Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.012750022, -32.012750022}
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