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Simplifying -10t2 + 40t + 2 = 0 Reorder the terms: 2 + 40t + -10t2 = 0 Solving 2 + 40t + -10t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(1 + 20t + -5t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(1 + 20t + -5t2)' equal to zero and attempt to solve: Simplifying 1 + 20t + -5t2 = 0 Solving 1 + 20t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -0.2 + -4t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -4t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -4t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -4t + t2 = 0 + 0.2 -4t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -4t + t2 = 0.2 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 = 0.2 + 4 Reorder the terms: 4 + -4t + t2 = 0.2 + 4 Combine like terms: 0.2 + 4 = 4.2 4 + -4t + t2 = 4.2 Factor a perfect square on the left side: (t + -2)(t + -2) = 4.2 Calculate the square root of the right side: 2.049390153 Break this problem into two subproblems by setting (t + -2) equal to 2.049390153 and -2.049390153.Subproblem 1
t + -2 = 2.049390153 Simplifying t + -2 = 2.049390153 Reorder the terms: -2 + t = 2.049390153 Solving -2 + t = 2.049390153 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 = 2.049390153 + 2 Combine like terms: -2 + 2 = 0 0 + t = 2.049390153 + 2 t = 2.049390153 + 2 Combine like terms: 2.049390153 + 2 = 4.049390153 t = 4.049390153 Simplifying t = 4.049390153Subproblem 2
t + -2 = -2.049390153 Simplifying t + -2 = -2.049390153 Reorder the terms: -2 + t = -2.049390153 Solving -2 + t = -2.049390153 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 = -2.049390153 + 2 Combine like terms: -2 + 2 = 0 0 + t = -2.049390153 + 2 t = -2.049390153 + 2 Combine like terms: -2.049390153 + 2 = -0.049390153 t = -0.049390153 Simplifying t = -0.049390153Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.049390153, -0.049390153}Solution
t = {4.049390153, -0.049390153}
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