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Simplifying 2t2 + -18t + 34 = 0 Reorder the terms: 34 + -18t + 2t2 = 0 Solving 34 + -18t + 2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(17 + -9t + t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(17 + -9t + t2)' equal to zero and attempt to solve: Simplifying 17 + -9t + t2 = 0 Solving 17 + -9t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-17' to each side of the equation. 17 + -9t + -17 + t2 = 0 + -17 Reorder the terms: 17 + -17 + -9t + t2 = 0 + -17 Combine like terms: 17 + -17 = 0 0 + -9t + t2 = 0 + -17 -9t + t2 = 0 + -17 Combine like terms: 0 + -17 = -17 -9t + t2 = -17 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = -17 + 20.25 Reorder the terms: 20.25 + -9t + t2 = -17 + 20.25 Combine like terms: -17 + 20.25 = 3.25 20.25 + -9t + t2 = 3.25 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 3.25 Calculate the square root of the right side: 1.802775638 Break this problem into two subproblems by setting (t + -4.5) equal to 1.802775638 and -1.802775638.Subproblem 1
t + -4.5 = 1.802775638 Simplifying t + -4.5 = 1.802775638 Reorder the terms: -4.5 + t = 1.802775638 Solving -4.5 + t = 1.802775638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 1.802775638 + 4.5 t = 1.802775638 + 4.5 Combine like terms: 1.802775638 + 4.5 = 6.302775638 t = 6.302775638 Simplifying t = 6.302775638Subproblem 2
t + -4.5 = -1.802775638 Simplifying t + -4.5 = -1.802775638 Reorder the terms: -4.5 + t = -1.802775638 Solving -4.5 + t = -1.802775638 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -1.802775638 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -1.802775638 + 4.5 t = -1.802775638 + 4.5 Combine like terms: -1.802775638 + 4.5 = 2.697224362 t = 2.697224362 Simplifying t = 2.697224362Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.302775638, 2.697224362}Solution
t = {6.302775638, 2.697224362}
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