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Simplifying 0 = -5t2 + 30t + 15 Reorder the terms: 0 = 15 + 30t + -5t2 Solving 0 = 15 + 30t + -5t2 Solving for variable 't'. Combine like terms: 0 + -15 = -15 -15 + -30t + 5t2 = 15 + 30t + -5t2 + -15 + -30t + 5t2 Reorder the terms: -15 + -30t + 5t2 = 15 + -15 + 30t + -30t + -5t2 + 5t2 Combine like terms: 15 + -15 = 0 -15 + -30t + 5t2 = 0 + 30t + -30t + -5t2 + 5t2 -15 + -30t + 5t2 = 30t + -30t + -5t2 + 5t2 Combine like terms: 30t + -30t = 0 -15 + -30t + 5t2 = 0 + -5t2 + 5t2 -15 + -30t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -15 + -30t + 5t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-3 + -6t + t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-3 + -6t + t2)' equal to zero and attempt to solve: Simplifying -3 + -6t + t2 = 0 Solving -3 + -6t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + -6t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + -6t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -6t + t2 = 0 + 3 -6t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 -6t + t2 = 3 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 = 3 + 9 Reorder the terms: 9 + -6t + t2 = 3 + 9 Combine like terms: 3 + 9 = 12 9 + -6t + t2 = 12 Factor a perfect square on the left side: (t + -3)(t + -3) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + -3) equal to 3.464101615 and -3.464101615.Subproblem 1
t + -3 = 3.464101615 Simplifying t + -3 = 3.464101615 Reorder the terms: -3 + t = 3.464101615 Solving -3 + t = 3.464101615 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 = 3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.464101615 + 3 t = 3.464101615 + 3 Combine like terms: 3.464101615 + 3 = 6.464101615 t = 6.464101615 Simplifying t = 6.464101615Subproblem 2
t + -3 = -3.464101615 Simplifying t + -3 = -3.464101615 Reorder the terms: -3 + t = -3.464101615 Solving -3 + t = -3.464101615 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 = -3.464101615 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.464101615 + 3 t = -3.464101615 + 3 Combine like terms: -3.464101615 + 3 = -0.464101615 t = -0.464101615 Simplifying t = -0.464101615Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.464101615, -0.464101615}Solution
t = {6.464101615, -0.464101615}
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