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Simplifying 4.9t2 + 10t + -65 = 0 Reorder the terms: -65 + 10t + 4.9t2 = 0 Solving -65 + 10t + 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'. -13.26530612 + 2.040816327t + t2 = 0 Move the constant term to the right: Add '13.26530612' to each side of the equation. -13.26530612 + 2.040816327t + 13.26530612 + t2 = 0 + 13.26530612 Reorder the terms: -13.26530612 + 13.26530612 + 2.040816327t + t2 = 0 + 13.26530612 Combine like terms: -13.26530612 + 13.26530612 = 0.00000000 0.00000000 + 2.040816327t + t2 = 0 + 13.26530612 2.040816327t + t2 = 0 + 13.26530612 Combine like terms: 0 + 13.26530612 = 13.26530612 2.040816327t + t2 = 13.26530612 The t term is 2.040816327t. Take half its coefficient (1.020408164). Square it (1.041232821) and add it to both sides. Add '1.041232821' to each side of the equation. 2.040816327t + 1.041232821 + t2 = 13.26530612 + 1.041232821 Reorder the terms: 1.041232821 + 2.040816327t + t2 = 13.26530612 + 1.041232821 Combine like terms: 13.26530612 + 1.041232821 = 14.306538941 1.041232821 + 2.040816327t + t2 = 14.306538941 Factor a perfect square on the left side: (t + 1.020408164)(t + 1.020408164) = 14.306538941 Calculate the square root of the right side: 3.78239857 Break this problem into two subproblems by setting (t + 1.020408164) equal to 3.78239857 and -3.78239857.Subproblem 1
t + 1.020408164 = 3.78239857 Simplifying t + 1.020408164 = 3.78239857 Reorder the terms: 1.020408164 + t = 3.78239857 Solving 1.020408164 + t = 3.78239857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + t = 3.78239857 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = 3.78239857 + -1.020408164 t = 3.78239857 + -1.020408164 Combine like terms: 3.78239857 + -1.020408164 = 2.761990406 t = 2.761990406 Simplifying t = 2.761990406Subproblem 2
t + 1.020408164 = -3.78239857 Simplifying t + 1.020408164 = -3.78239857 Reorder the terms: 1.020408164 + t = -3.78239857 Solving 1.020408164 + t = -3.78239857 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.020408164' to each side of the equation. 1.020408164 + -1.020408164 + t = -3.78239857 + -1.020408164 Combine like terms: 1.020408164 + -1.020408164 = 0.000000000 0.000000000 + t = -3.78239857 + -1.020408164 t = -3.78239857 + -1.020408164 Combine like terms: -3.78239857 + -1.020408164 = -4.802806734 t = -4.802806734 Simplifying t = -4.802806734Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.761990406, -4.802806734}
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