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Simplifying -2t2 + 112t + 190 = 0 Reorder the terms: 190 + 112t + -2t2 = 0 Solving 190 + 112t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(95 + 56t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(95 + 56t + -1t2)' equal to zero and attempt to solve: Simplifying 95 + 56t + -1t2 = 0 Solving 95 + 56t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -95 + -56t + t2 = 0 Move the constant term to the right: Add '95' to each side of the equation. -95 + -56t + 95 + t2 = 0 + 95 Reorder the terms: -95 + 95 + -56t + t2 = 0 + 95 Combine like terms: -95 + 95 = 0 0 + -56t + t2 = 0 + 95 -56t + t2 = 0 + 95 Combine like terms: 0 + 95 = 95 -56t + t2 = 95 The t term is -56t. Take half its coefficient (-28). Square it (784) and add it to both sides. Add '784' to each side of the equation. -56t + 784 + t2 = 95 + 784 Reorder the terms: 784 + -56t + t2 = 95 + 784 Combine like terms: 95 + 784 = 879 784 + -56t + t2 = 879 Factor a perfect square on the left side: (t + -28)(t + -28) = 879 Calculate the square root of the right side: 29.647934161 Break this problem into two subproblems by setting (t + -28) equal to 29.647934161 and -29.647934161.Subproblem 1
t + -28 = 29.647934161 Simplifying t + -28 = 29.647934161 Reorder the terms: -28 + t = 29.647934161 Solving -28 + t = 29.647934161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + t = 29.647934161 + 28 Combine like terms: -28 + 28 = 0 0 + t = 29.647934161 + 28 t = 29.647934161 + 28 Combine like terms: 29.647934161 + 28 = 57.647934161 t = 57.647934161 Simplifying t = 57.647934161Subproblem 2
t + -28 = -29.647934161 Simplifying t + -28 = -29.647934161 Reorder the terms: -28 + t = -29.647934161 Solving -28 + t = -29.647934161 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '28' to each side of the equation. -28 + 28 + t = -29.647934161 + 28 Combine like terms: -28 + 28 = 0 0 + t = -29.647934161 + 28 t = -29.647934161 + 28 Combine like terms: -29.647934161 + 28 = -1.647934161 t = -1.647934161 Simplifying t = -1.647934161Solution
The solution to the problem is based on the solutions from the subproblems. t = {57.647934161, -1.647934161}Solution
t = {57.647934161, -1.647934161}
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