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Simplifying 0 = 38 + -3t + -5t2 Solving 0 = 38 + -3t + -5t2 Solving for variable 't'. Combine like terms: 0 + -38 = -38 -38 + 3t + 5t2 = 38 + -3t + -5t2 + -38 + 3t + 5t2 Reorder the terms: -38 + 3t + 5t2 = 38 + -38 + -3t + 3t + -5t2 + 5t2 Combine like terms: 38 + -38 = 0 -38 + 3t + 5t2 = 0 + -3t + 3t + -5t2 + 5t2 -38 + 3t + 5t2 = -3t + 3t + -5t2 + 5t2 Combine like terms: -3t + 3t = 0 -38 + 3t + 5t2 = 0 + -5t2 + 5t2 -38 + 3t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -38 + 3t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.6 + 0.6t + t2 = 0 Move the constant term to the right: Add '7.6' to each side of the equation. -7.6 + 0.6t + 7.6 + t2 = 0 + 7.6 Reorder the terms: -7.6 + 7.6 + 0.6t + t2 = 0 + 7.6 Combine like terms: -7.6 + 7.6 = 0.0 0.0 + 0.6t + t2 = 0 + 7.6 0.6t + t2 = 0 + 7.6 Combine like terms: 0 + 7.6 = 7.6 0.6t + t2 = 7.6 The t term is 0.6t. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6t + 0.09 + t2 = 7.6 + 0.09 Reorder the terms: 0.09 + 0.6t + t2 = 7.6 + 0.09 Combine like terms: 7.6 + 0.09 = 7.69 0.09 + 0.6t + t2 = 7.69 Factor a perfect square on the left side: (t + 0.3)(t + 0.3) = 7.69 Calculate the square root of the right side: 2.773084925 Break this problem into two subproblems by setting (t + 0.3) equal to 2.773084925 and -2.773084925.Subproblem 1
t + 0.3 = 2.773084925 Simplifying t + 0.3 = 2.773084925 Reorder the terms: 0.3 + t = 2.773084925 Solving 0.3 + t = 2.773084925 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + t = 2.773084925 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + t = 2.773084925 + -0.3 t = 2.773084925 + -0.3 Combine like terms: 2.773084925 + -0.3 = 2.473084925 t = 2.473084925 Simplifying t = 2.473084925Subproblem 2
t + 0.3 = -2.773084925 Simplifying t + 0.3 = -2.773084925 Reorder the terms: 0.3 + t = -2.773084925 Solving 0.3 + t = -2.773084925 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + t = -2.773084925 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + t = -2.773084925 + -0.3 t = -2.773084925 + -0.3 Combine like terms: -2.773084925 + -0.3 = -3.073084925 t = -3.073084925 Simplifying t = -3.073084925Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.473084925, -3.073084925}
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