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Simplifying 5t2 + -6t + -100 = 0 Reorder the terms: -100 + -6t + 5t2 = 0 Solving -100 + -6t + 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'. -20 + -1.2t + t2 = 0 Move the constant term to the right: Add '20' to each side of the equation. -20 + -1.2t + 20 + t2 = 0 + 20 Reorder the terms: -20 + 20 + -1.2t + t2 = 0 + 20 Combine like terms: -20 + 20 = 0 0 + -1.2t + t2 = 0 + 20 -1.2t + t2 = 0 + 20 Combine like terms: 0 + 20 = 20 -1.2t + t2 = 20 The t term is -1.2t. Take half its coefficient (-0.6). Square it (0.36) and add it to both sides. Add '0.36' to each side of the equation. -1.2t + 0.36 + t2 = 20 + 0.36 Reorder the terms: 0.36 + -1.2t + t2 = 20 + 0.36 Combine like terms: 20 + 0.36 = 20.36 0.36 + -1.2t + t2 = 20.36 Factor a perfect square on the left side: (t + -0.6)(t + -0.6) = 20.36 Calculate the square root of the right side: 4.512205669 Break this problem into two subproblems by setting (t + -0.6) equal to 4.512205669 and -4.512205669.Subproblem 1
t + -0.6 = 4.512205669 Simplifying t + -0.6 = 4.512205669 Reorder the terms: -0.6 + t = 4.512205669 Solving -0.6 + t = 4.512205669 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = 4.512205669 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = 4.512205669 + 0.6 t = 4.512205669 + 0.6 Combine like terms: 4.512205669 + 0.6 = 5.112205669 t = 5.112205669 Simplifying t = 5.112205669Subproblem 2
t + -0.6 = -4.512205669 Simplifying t + -0.6 = -4.512205669 Reorder the terms: -0.6 + t = -4.512205669 Solving -0.6 + t = -4.512205669 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.6' to each side of the equation. -0.6 + 0.6 + t = -4.512205669 + 0.6 Combine like terms: -0.6 + 0.6 = 0.0 0.0 + t = -4.512205669 + 0.6 t = -4.512205669 + 0.6 Combine like terms: -4.512205669 + 0.6 = -3.912205669 t = -3.912205669 Simplifying t = -3.912205669Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.112205669, -3.912205669}
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