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Simplifying 30t2 + -19t = 36 Reorder the terms: -19t + 30t2 = 36 Solving -19t + 30t2 = 36 Solving for variable 't'. Reorder the terms: -36 + -19t + 30t2 = 36 + -36 Combine like terms: 36 + -36 = 0 -36 + -19t + 30t2 = 0 Begin completing the square. Divide all terms by 30 the coefficient of the squared term: Divide each side by '30'. -1.2 + -0.6333333333t + t2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + -0.6333333333t + 1.2 + t2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + -0.6333333333t + t2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + -0.6333333333t + t2 = 0 + 1.2 -0.6333333333t + t2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 -0.6333333333t + t2 = 1.2 The t term is -0.6333333333t. Take half its coefficient (-0.3166666667). Square it (0.1002777778) and add it to both sides. Add '0.1002777778' to each side of the equation. -0.6333333333t + 0.1002777778 + t2 = 1.2 + 0.1002777778 Reorder the terms: 0.1002777778 + -0.6333333333t + t2 = 1.2 + 0.1002777778 Combine like terms: 1.2 + 0.1002777778 = 1.3002777778 0.1002777778 + -0.6333333333t + t2 = 1.3002777778 Factor a perfect square on the left side: (t + -0.3166666667)(t + -0.3166666667) = 1.3002777778 Calculate the square root of the right side: 1.140297232 Break this problem into two subproblems by setting (t + -0.3166666667) equal to 1.140297232 and -1.140297232.Subproblem 1
t + -0.3166666667 = 1.140297232 Simplifying t + -0.3166666667 = 1.140297232 Reorder the terms: -0.3166666667 + t = 1.140297232 Solving -0.3166666667 + t = 1.140297232 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3166666667' to each side of the equation. -0.3166666667 + 0.3166666667 + t = 1.140297232 + 0.3166666667 Combine like terms: -0.3166666667 + 0.3166666667 = 0.0000000000 0.0000000000 + t = 1.140297232 + 0.3166666667 t = 1.140297232 + 0.3166666667 Combine like terms: 1.140297232 + 0.3166666667 = 1.4569638987 t = 1.4569638987 Simplifying t = 1.4569638987Subproblem 2
t + -0.3166666667 = -1.140297232 Simplifying t + -0.3166666667 = -1.140297232 Reorder the terms: -0.3166666667 + t = -1.140297232 Solving -0.3166666667 + t = -1.140297232 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.3166666667' to each side of the equation. -0.3166666667 + 0.3166666667 + t = -1.140297232 + 0.3166666667 Combine like terms: -0.3166666667 + 0.3166666667 = 0.0000000000 0.0000000000 + t = -1.140297232 + 0.3166666667 t = -1.140297232 + 0.3166666667 Combine like terms: -1.140297232 + 0.3166666667 = -0.8236305653 t = -0.8236305653 Simplifying t = -0.8236305653Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.4569638987, -0.8236305653}
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