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Simplifying 16t2 + 250t + 60 = 0 Reorder the terms: 60 + 250t + 16t2 = 0 Solving 60 + 250t + 16t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(30 + 125t + 8t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(30 + 125t + 8t2)' equal to zero and attempt to solve: Simplifying 30 + 125t + 8t2 = 0 Solving 30 + 125t + 8t2 = 0 Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 3.75 + 15.625t + t2 = 0 Move the constant term to the right: Add '-3.75' to each side of the equation. 3.75 + 15.625t + -3.75 + t2 = 0 + -3.75 Reorder the terms: 3.75 + -3.75 + 15.625t + t2 = 0 + -3.75 Combine like terms: 3.75 + -3.75 = 0.00 0.00 + 15.625t + t2 = 0 + -3.75 15.625t + t2 = 0 + -3.75 Combine like terms: 0 + -3.75 = -3.75 15.625t + t2 = -3.75 The t term is 15.625t. Take half its coefficient (7.8125). Square it (61.03515625) and add it to both sides. Add '61.03515625' to each side of the equation. 15.625t + 61.03515625 + t2 = -3.75 + 61.03515625 Reorder the terms: 61.03515625 + 15.625t + t2 = -3.75 + 61.03515625 Combine like terms: -3.75 + 61.03515625 = 57.28515625 61.03515625 + 15.625t + t2 = 57.28515625 Factor a perfect square on the left side: (t + 7.8125)(t + 7.8125) = 57.28515625 Calculate the square root of the right side: 7.568695809 Break this problem into two subproblems by setting (t + 7.8125) equal to 7.568695809 and -7.568695809.Subproblem 1
t + 7.8125 = 7.568695809 Simplifying t + 7.8125 = 7.568695809 Reorder the terms: 7.8125 + t = 7.568695809 Solving 7.8125 + t = 7.568695809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.8125' to each side of the equation. 7.8125 + -7.8125 + t = 7.568695809 + -7.8125 Combine like terms: 7.8125 + -7.8125 = 0.0000 0.0000 + t = 7.568695809 + -7.8125 t = 7.568695809 + -7.8125 Combine like terms: 7.568695809 + -7.8125 = -0.243804191 t = -0.243804191 Simplifying t = -0.243804191Subproblem 2
t + 7.8125 = -7.568695809 Simplifying t + 7.8125 = -7.568695809 Reorder the terms: 7.8125 + t = -7.568695809 Solving 7.8125 + t = -7.568695809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7.8125' to each side of the equation. 7.8125 + -7.8125 + t = -7.568695809 + -7.8125 Combine like terms: 7.8125 + -7.8125 = 0.0000 0.0000 + t = -7.568695809 + -7.8125 t = -7.568695809 + -7.8125 Combine like terms: -7.568695809 + -7.8125 = -15.381195809 t = -15.381195809 Simplifying t = -15.381195809Solution
The solution to the problem is based on the solutions from the subproblems. t = {-0.243804191, -15.381195809}Solution
t = {-0.243804191, -15.381195809}
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