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Simplifying 0 = -2t2 + -14t + 14 Reorder the terms: 0 = 14 + -14t + -2t2 Solving 0 = 14 + -14t + -2t2 Solving for variable 't'. Combine like terms: 0 + -14 = -14 -14 + 14t + 2t2 = 14 + -14t + -2t2 + -14 + 14t + 2t2 Reorder the terms: -14 + 14t + 2t2 = 14 + -14 + -14t + 14t + -2t2 + 2t2 Combine like terms: 14 + -14 = 0 -14 + 14t + 2t2 = 0 + -14t + 14t + -2t2 + 2t2 -14 + 14t + 2t2 = -14t + 14t + -2t2 + 2t2 Combine like terms: -14t + 14t = 0 -14 + 14t + 2t2 = 0 + -2t2 + 2t2 -14 + 14t + 2t2 = -2t2 + 2t2 Combine like terms: -2t2 + 2t2 = 0 -14 + 14t + 2t2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-7 + 7t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-7 + 7t + t2)' equal to zero and attempt to solve: Simplifying -7 + 7t + t2 = 0 Solving -7 + 7t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '7' to each side of the equation. -7 + 7t + 7 + t2 = 0 + 7 Reorder the terms: -7 + 7 + 7t + t2 = 0 + 7 Combine like terms: -7 + 7 = 0 0 + 7t + t2 = 0 + 7 7t + t2 = 0 + 7 Combine like terms: 0 + 7 = 7 7t + t2 = 7 The t term is 7t. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7t + 12.25 + t2 = 7 + 12.25 Reorder the terms: 12.25 + 7t + t2 = 7 + 12.25 Combine like terms: 7 + 12.25 = 19.25 12.25 + 7t + t2 = 19.25 Factor a perfect square on the left side: (t + 3.5)(t + 3.5) = 19.25 Calculate the square root of the right side: 4.387482194 Break this problem into two subproblems by setting (t + 3.5) equal to 4.387482194 and -4.387482194.Subproblem 1
t + 3.5 = 4.387482194 Simplifying t + 3.5 = 4.387482194 Reorder the terms: 3.5 + t = 4.387482194 Solving 3.5 + t = 4.387482194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = 4.387482194 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = 4.387482194 + -3.5 t = 4.387482194 + -3.5 Combine like terms: 4.387482194 + -3.5 = 0.887482194 t = 0.887482194 Simplifying t = 0.887482194Subproblem 2
t + 3.5 = -4.387482194 Simplifying t + 3.5 = -4.387482194 Reorder the terms: 3.5 + t = -4.387482194 Solving 3.5 + t = -4.387482194 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + t = -4.387482194 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + t = -4.387482194 + -3.5 t = -4.387482194 + -3.5 Combine like terms: -4.387482194 + -3.5 = -7.887482194 t = -7.887482194 Simplifying t = -7.887482194Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.887482194, -7.887482194}Solution
t = {0.887482194, -7.887482194}
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