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Simplifying 0 = 15t2 + -120t + -190 Reorder the terms: 0 = -190 + -120t + 15t2 Solving 0 = -190 + -120t + 15t2 Solving for variable 't'. Combine like terms: 0 + 190 = 190 190 + 120t + -15t2 = -190 + -120t + 15t2 + 190 + 120t + -15t2 Reorder the terms: 190 + 120t + -15t2 = -190 + 190 + -120t + 120t + 15t2 + -15t2 Combine like terms: -190 + 190 = 0 190 + 120t + -15t2 = 0 + -120t + 120t + 15t2 + -15t2 190 + 120t + -15t2 = -120t + 120t + 15t2 + -15t2 Combine like terms: -120t + 120t = 0 190 + 120t + -15t2 = 0 + 15t2 + -15t2 190 + 120t + -15t2 = 15t2 + -15t2 Combine like terms: 15t2 + -15t2 = 0 190 + 120t + -15t2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(38 + 24t + -3t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(38 + 24t + -3t2)' equal to zero and attempt to solve: Simplifying 38 + 24t + -3t2 = 0 Solving 38 + 24t + -3t2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. -12.66666667 + -8t + t2 = 0 Move the constant term to the right: Add '12.66666667' to each side of the equation. -12.66666667 + -8t + 12.66666667 + t2 = 0 + 12.66666667 Reorder the terms: -12.66666667 + 12.66666667 + -8t + t2 = 0 + 12.66666667 Combine like terms: -12.66666667 + 12.66666667 = 0.00000000 0.00000000 + -8t + t2 = 0 + 12.66666667 -8t + t2 = 0 + 12.66666667 Combine like terms: 0 + 12.66666667 = 12.66666667 -8t + t2 = 12.66666667 The t term is -8t. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8t + 16 + t2 = 12.66666667 + 16 Reorder the terms: 16 + -8t + t2 = 12.66666667 + 16 Combine like terms: 12.66666667 + 16 = 28.66666667 16 + -8t + t2 = 28.66666667 Factor a perfect square on the left side: (t + -4)(t + -4) = 28.66666667 Calculate the square root of the right side: 5.354126135 Break this problem into two subproblems by setting (t + -4) equal to 5.354126135 and -5.354126135.Subproblem 1
t + -4 = 5.354126135 Simplifying t + -4 = 5.354126135 Reorder the terms: -4 + t = 5.354126135 Solving -4 + t = 5.354126135 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = 5.354126135 + 4 Combine like terms: -4 + 4 = 0 0 + t = 5.354126135 + 4 t = 5.354126135 + 4 Combine like terms: 5.354126135 + 4 = 9.354126135 t = 9.354126135 Simplifying t = 9.354126135Subproblem 2
t + -4 = -5.354126135 Simplifying t + -4 = -5.354126135 Reorder the terms: -4 + t = -5.354126135 Solving -4 + t = -5.354126135 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + t = -5.354126135 + 4 Combine like terms: -4 + 4 = 0 0 + t = -5.354126135 + 4 t = -5.354126135 + 4 Combine like terms: -5.354126135 + 4 = -1.354126135 t = -1.354126135 Simplifying t = -1.354126135Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.354126135, -1.354126135}Solution
t = {9.354126135, -1.354126135}
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