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Simplifying -5t2 + 20t + 50 = 0 Reorder the terms: 50 + 20t + -5t2 = 0 Solving 50 + 20t + -5t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '5'. 5(10 + 4t + -1t2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(10 + 4t + -1t2)' equal to zero and attempt to solve: Simplifying 10 + 4t + -1t2 = 0 Solving 10 + 4t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -10 + -4t + t2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + -4t + 10 + t2 = 0 + 10 Reorder the terms: -10 + 10 + -4t + t2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -4t + t2 = 0 + 10 -4t + t2 = 0 + 10 Combine like terms: 0 + 10 = 10 -4t + t2 = 10 The t term is -4t. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4t + 4 + t2 = 10 + 4 Reorder the terms: 4 + -4t + t2 = 10 + 4 Combine like terms: 10 + 4 = 14 4 + -4t + t2 = 14 Factor a perfect square on the left side: (t + -2)(t + -2) = 14 Calculate the square root of the right side: 3.741657387 Break this problem into two subproblems by setting (t + -2) equal to 3.741657387 and -3.741657387.Subproblem 1
t + -2 = 3.741657387 Simplifying t + -2 = 3.741657387 Reorder the terms: -2 + t = 3.741657387 Solving -2 + t = 3.741657387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = 3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + t = 3.741657387 + 2 t = 3.741657387 + 2 Combine like terms: 3.741657387 + 2 = 5.741657387 t = 5.741657387 Simplifying t = 5.741657387Subproblem 2
t + -2 = -3.741657387 Simplifying t + -2 = -3.741657387 Reorder the terms: -2 + t = -3.741657387 Solving -2 + t = -3.741657387 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + t = -3.741657387 + 2 Combine like terms: -2 + 2 = 0 0 + t = -3.741657387 + 2 t = -3.741657387 + 2 Combine like terms: -3.741657387 + 2 = -1.741657387 t = -1.741657387 Simplifying t = -1.741657387Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.741657387, -1.741657387}Solution
t = {5.741657387, -1.741657387}
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