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Simplifying -2t2 + -2t + 130 = 0 Reorder the terms: 130 + -2t + -2t2 = 0 Solving 130 + -2t + -2t2 = 0 Solving for variable 't'. Factor out the Greatest Common Factor (GCF), '2'. 2(65 + -1t + -1t2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(65 + -1t + -1t2)' equal to zero and attempt to solve: Simplifying 65 + -1t + -1t2 = 0 Solving 65 + -1t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -65 + t + t2 = 0 Move the constant term to the right: Add '65' to each side of the equation. -65 + t + 65 + t2 = 0 + 65 Reorder the terms: -65 + 65 + t + t2 = 0 + 65 Combine like terms: -65 + 65 = 0 0 + t + t2 = 0 + 65 t + t2 = 0 + 65 Combine like terms: 0 + 65 = 65 t + t2 = 65 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 65 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 65 + 0.25 Combine like terms: 65 + 0.25 = 65.25 1.25 + t2 = 65.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 65.25 Calculate the square root of the right side: 8.077747211 Break this problem into two subproblems by setting (t + 0.5) equal to 8.077747211 and -8.077747211.Subproblem 1
t + 0.5 = 8.077747211 Simplifying t + 0.5 = 8.077747211 Reorder the terms: 0.5 + t = 8.077747211 Solving 0.5 + t = 8.077747211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 8.077747211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 8.077747211 + -0.5 t = 8.077747211 + -0.5 Combine like terms: 8.077747211 + -0.5 = 7.577747211 t = 7.577747211 Simplifying t = 7.577747211Subproblem 2
t + 0.5 = -8.077747211 Simplifying t + 0.5 = -8.077747211 Reorder the terms: 0.5 + t = -8.077747211 Solving 0.5 + t = -8.077747211 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -8.077747211 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -8.077747211 + -0.5 t = -8.077747211 + -0.5 Combine like terms: -8.077747211 + -0.5 = -8.577747211 t = -8.577747211 Simplifying t = -8.577747211Solution
The solution to the problem is based on the solutions from the subproblems. t = {7.577747211, -8.577747211}Solution
t = {7.577747211, -8.577747211}
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