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Simplifying 5t2 + 12.5t + -136 = 0 Reorder the terms: -136 + 12.5t + 5t2 = 0 Solving -136 + 12.5t + 5t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -27.2 + 2.5t + t2 = 0 Move the constant term to the right: Add '27.2' to each side of the equation. -27.2 + 2.5t + 27.2 + t2 = 0 + 27.2 Reorder the terms: -27.2 + 27.2 + 2.5t + t2 = 0 + 27.2 Combine like terms: -27.2 + 27.2 = 0.0 0.0 + 2.5t + t2 = 0 + 27.2 2.5t + t2 = 0 + 27.2 Combine like terms: 0 + 27.2 = 27.2 2.5t + t2 = 27.2 The t term is 2.5t. Take half its coefficient (1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. 2.5t + 1.5625 + t2 = 27.2 + 1.5625 Reorder the terms: 1.5625 + 2.5t + t2 = 27.2 + 1.5625 Combine like terms: 27.2 + 1.5625 = 28.7625 1.5625 + 2.5t + t2 = 28.7625 Factor a perfect square on the left side: (t + 1.25)(t + 1.25) = 28.7625 Calculate the square root of the right side: 5.363068152 Break this problem into two subproblems by setting (t + 1.25) equal to 5.363068152 and -5.363068152.Subproblem 1
t + 1.25 = 5.363068152 Simplifying t + 1.25 = 5.363068152 Reorder the terms: 1.25 + t = 5.363068152 Solving 1.25 + t = 5.363068152 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = 5.363068152 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = 5.363068152 + -1.25 t = 5.363068152 + -1.25 Combine like terms: 5.363068152 + -1.25 = 4.113068152 t = 4.113068152 Simplifying t = 4.113068152Subproblem 2
t + 1.25 = -5.363068152 Simplifying t + 1.25 = -5.363068152 Reorder the terms: 1.25 + t = -5.363068152 Solving 1.25 + t = -5.363068152 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1.25' to each side of the equation. 1.25 + -1.25 + t = -5.363068152 + -1.25 Combine like terms: 1.25 + -1.25 = 0.00 0.00 + t = -5.363068152 + -1.25 t = -5.363068152 + -1.25 Combine like terms: -5.363068152 + -1.25 = -6.613068152 t = -6.613068152 Simplifying t = -6.613068152Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.113068152, -6.613068152}
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