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Simplifying (0.5 + 7t)(0.0625 + -8t) = 0 Multiply (0.5 + 7t) * (0.0625 + -8t) (0.5(0.0625 + -8t) + 7t * (0.0625 + -8t)) = 0 ((0.0625 * 0.5 + -8t * 0.5) + 7t * (0.0625 + -8t)) = 0 ((0.03125 + -4t) + 7t * (0.0625 + -8t)) = 0 (0.03125 + -4t + (0.0625 * 7t + -8t * 7t)) = 0 (0.03125 + -4t + (0.4375t + -56t2)) = 0 Combine like terms: -4t + 0.4375t = -3.5625t (0.03125 + -3.5625t + -56t2) = 0 Solving 0.03125 + -3.5625t + -56t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -56 the coefficient of the squared term: Divide each side by '-56'. -0.0005580357143 + 0.06361607143t + t2 = 0 Move the constant term to the right: Add '0.0005580357143' to each side of the equation. -0.0005580357143 + 0.06361607143t + 0.0005580357143 + t2 = 0 + 0.0005580357143 Reorder the terms: -0.0005580357143 + 0.0005580357143 + 0.06361607143t + t2 = 0 + 0.0005580357143 Combine like terms: -0.0005580357143 + 0.0005580357143 = 0.0000000000000 0.0000000000000 + 0.06361607143t + t2 = 0 + 0.0005580357143 0.06361607143t + t2 = 0 + 0.0005580357143 Combine like terms: 0 + 0.0005580357143 = 0.0005580357143 0.06361607143t + t2 = 0.0005580357143 The t term is 0.06361607143t. Take half its coefficient (0.03180803572). Square it (0.001011751136) and add it to both sides. Add '0.001011751136' to each side of the equation. 0.06361607143t + 0.001011751136 + t2 = 0.0005580357143 + 0.001011751136 Reorder the terms: 0.001011751136 + 0.06361607143t + t2 = 0.0005580357143 + 0.001011751136 Combine like terms: 0.0005580357143 + 0.001011751136 = 0.0015697868503 0.001011751136 + 0.06361607143t + t2 = 0.0015697868503 Factor a perfect square on the left side: (t + 0.03180803572)(t + 0.03180803572) = 0.0015697868503 Calculate the square root of the right side: 0.039620536 Break this problem into two subproblems by setting (t + 0.03180803572) equal to 0.039620536 and -0.039620536.Subproblem 1
t + 0.03180803572 = 0.039620536 Simplifying t + 0.03180803572 = 0.039620536 Reorder the terms: 0.03180803572 + t = 0.039620536 Solving 0.03180803572 + t = 0.039620536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03180803572' to each side of the equation. 0.03180803572 + -0.03180803572 + t = 0.039620536 + -0.03180803572 Combine like terms: 0.03180803572 + -0.03180803572 = 0.00000000000 0.00000000000 + t = 0.039620536 + -0.03180803572 t = 0.039620536 + -0.03180803572 Combine like terms: 0.039620536 + -0.03180803572 = 0.00781250028 t = 0.00781250028 Simplifying t = 0.00781250028Subproblem 2
t + 0.03180803572 = -0.039620536 Simplifying t + 0.03180803572 = -0.039620536 Reorder the terms: 0.03180803572 + t = -0.039620536 Solving 0.03180803572 + t = -0.039620536 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.03180803572' to each side of the equation. 0.03180803572 + -0.03180803572 + t = -0.039620536 + -0.03180803572 Combine like terms: 0.03180803572 + -0.03180803572 = 0.00000000000 0.00000000000 + t = -0.039620536 + -0.03180803572 t = -0.039620536 + -0.03180803572 Combine like terms: -0.039620536 + -0.03180803572 = -0.07142857172 t = -0.07142857172 Simplifying t = -0.07142857172Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.00781250028, -0.07142857172}
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