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Simplifying -15t2 + 90t + 75 = 0 Reorder the terms: 75 + 90t + -15t2 = 0 Solving 75 + 90t + -15t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '15'. 15(5 + 6t + -1t2) = 0 Ignore the factor 15.Subproblem 1
Set the factor '(5 + 6t + -1t2)' equal to zero and attempt to solve: Simplifying 5 + 6t + -1t2 = 0 Solving 5 + 6t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -5 + -6t + t2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -6t + 5 + t2 = 0 + 5 Reorder the terms: -5 + 5 + -6t + t2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -6t + t2 = 0 + 5 -6t + t2 = 0 + 5 Combine like terms: 0 + 5 = 5 -6t + t2 = 5 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 = 5 + 9 Reorder the terms: 9 + -6t + t2 = 5 + 9 Combine like terms: 5 + 9 = 14 9 + -6t + t2 = 14 Factor a perfect square on the left side: (t + -3)(t + -3) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (t + -3) equal to 3.741657387 and -3.741657387.Subproblem 1
t + -3 = 3.741657387 Simplifying t + -3 = 3.741657387 Reorder the terms: -3 + t = 3.741657387 Solving -3 + t = 3.741657387 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 = 3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + t = 3.741657387 + 3 t = 3.741657387 + 3 Combine like terms: 3.741657387 + 3 = 6.741657387 t = 6.741657387 Simplifying t = 6.741657387Subproblem 2
t + -3 = -3.741657387 Simplifying t + -3 = -3.741657387 Reorder the terms: -3 + t = -3.741657387 Solving -3 + t = -3.741657387 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 = -3.741657387 + 3 Combine like terms: -3 + 3 = 0 0 + t = -3.741657387 + 3 t = -3.741657387 + 3 Combine like terms: -3.741657387 + 3 = -0.741657387 t = -0.741657387 Simplifying t = -0.741657387Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.741657387, -0.741657387}Solution
t = {6.741657387, -0.741657387}
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