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Simplifying 8t2 + -32t + -200 = 0 Reorder the terms: -200 + -32t + 8t2 = 0 Solving -200 + -32t + 8t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '8'. 8(-25 + -4t + t2) = 0 Ignore the factor 8.Subproblem 1
Set the factor '(-25 + -4t + t2)' equal to zero and attempt to solve: Simplifying -25 + -4t + t2 = 0 Solving -25 + -4t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '25' to each side of the equation. -25 + -4t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + -4t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -4t + t2 = 0 + 25 -4t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 -4t + t2 = 25 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 = 25 + 4 Reorder the terms: 4 + -4t + t2 = 25 + 4 Combine like terms: 25 + 4 = 29 4 + -4t + t2 = 29 Factor a perfect square on the left side: (t + -2)(t + -2) = 29 Calculate the square root of the right side: 5.385164807 Break this problem into two subproblems by setting (t + -2) equal to 5.385164807 and -5.385164807.Subproblem 1
t + -2 = 5.385164807 Simplifying t + -2 = 5.385164807 Reorder the terms: -2 + t = 5.385164807 Solving -2 + t = 5.385164807 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 = 5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + t = 5.385164807 + 2 t = 5.385164807 + 2 Combine like terms: 5.385164807 + 2 = 7.385164807 t = 7.385164807 Simplifying t = 7.385164807Subproblem 2
t + -2 = -5.385164807 Simplifying t + -2 = -5.385164807 Reorder the terms: -2 + t = -5.385164807 Solving -2 + t = -5.385164807 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 = -5.385164807 + 2 Combine like terms: -2 + 2 = 0 0 + t = -5.385164807 + 2 t = -5.385164807 + 2 Combine like terms: -5.385164807 + 2 = -3.385164807 t = -3.385164807 Simplifying t = -3.385164807Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.385164807, -3.385164807}Solution
t = {7.385164807, -3.385164807}
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