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Simplifying 16t2 + 636t + -476 = 0 Reorder the terms: -476 + 636t + 16t2 = 0 Solving -476 + 636t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '4'. 4(-119 + 159t + 4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-119 + 159t + 4t2)' equal to zero and attempt to solve: Simplifying -119 + 159t + 4t2 = 0 Solving -119 + 159t + 4t2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -29.75 + 39.75t + t2 = 0 Move the constant term to the right: Add '29.75' to each side of the equation. -29.75 + 39.75t + 29.75 + t2 = 0 + 29.75 Reorder the terms: -29.75 + 29.75 + 39.75t + t2 = 0 + 29.75 Combine like terms: -29.75 + 29.75 = 0.00 0.00 + 39.75t + t2 = 0 + 29.75 39.75t + t2 = 0 + 29.75 Combine like terms: 0 + 29.75 = 29.75 39.75t + t2 = 29.75 The t term is 39.75t. Take half its coefficient (19.875). Square it (395.015625) and add it to both sides. Add '395.015625' to each side of the equation. 39.75t + 395.015625 + t2 = 29.75 + 395.015625 Reorder the terms: 395.015625 + 39.75t + t2 = 29.75 + 395.015625 Combine like terms: 29.75 + 395.015625 = 424.765625 395.015625 + 39.75t + t2 = 424.765625 Factor a perfect square on the left side: (t + 19.875)(t + 19.875) = 424.765625 Calculate the square root of the right side: 20.609842915 Break this problem into two subproblems by setting (t + 19.875) equal to 20.609842915 and -20.609842915.Subproblem 1
t + 19.875 = 20.609842915 Simplifying t + 19.875 = 20.609842915 Reorder the terms: 19.875 + t = 20.609842915 Solving 19.875 + t = 20.609842915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.875' to each side of the equation. 19.875 + -19.875 + t = 20.609842915 + -19.875 Combine like terms: 19.875 + -19.875 = 0.000 0.000 + t = 20.609842915 + -19.875 t = 20.609842915 + -19.875 Combine like terms: 20.609842915 + -19.875 = 0.734842915 t = 0.734842915 Simplifying t = 0.734842915Subproblem 2
t + 19.875 = -20.609842915 Simplifying t + 19.875 = -20.609842915 Reorder the terms: 19.875 + t = -20.609842915 Solving 19.875 + t = -20.609842915 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-19.875' to each side of the equation. 19.875 + -19.875 + t = -20.609842915 + -19.875 Combine like terms: 19.875 + -19.875 = 0.000 0.000 + t = -20.609842915 + -19.875 t = -20.609842915 + -19.875 Combine like terms: -20.609842915 + -19.875 = -40.484842915 t = -40.484842915 Simplifying t = -40.484842915Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.734842915, -40.484842915}Solution
t = {0.734842915, -40.484842915}
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