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Simplifying -10 + 30t + -5t2 = 0 Solving -10 + 30t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(-2 + 6t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-2 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying -2 + 6t + -1t2 = 0 Solving -2 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2 + -6t + t2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + -6t + -2 + t2 = 0 + -2 Reorder the terms: 2 + -2 + -6t + t2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -6t + t2 = 0 + -2 -6t + t2 = 0 + -2 Combine like terms: 0 + -2 = -2 -6t + t2 = -2 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = -2 + 9 Reorder the terms: 9 + -6t + t2 = -2 + 9 Combine like terms: -2 + 9 = 7 9 + -6t + t2 = 7 Factor a perfect square on the left side: (t + -3)(t + -3) = 7 Calculate the square root of the right side: 2.645751311 Break this problem into two subproblems by setting (t + -3) equal to 2.645751311 and -2.645751311.Subproblem 1
t + -3 = 2.645751311 Simplifying t + -3 = 2.645751311 Reorder the terms: -3 + t = 2.645751311 Solving -3 + t = 2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + t = 2.645751311 + 3 t = 2.645751311 + 3 Combine like terms: 2.645751311 + 3 = 5.645751311 t = 5.645751311 Simplifying t = 5.645751311Subproblem 2
t + -3 = -2.645751311 Simplifying t + -3 = -2.645751311 Reorder the terms: -3 + t = -2.645751311 Solving -3 + t = -2.645751311 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -2.645751311 + 3 Combine like terms: -3 + 3 = 0 0 + t = -2.645751311 + 3 t = -2.645751311 + 3 Combine like terms: -2.645751311 + 3 = 0.354248689 t = 0.354248689 Simplifying t = 0.354248689Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.645751311, 0.354248689}Solution
t = {5.645751311, 0.354248689}
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