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Simplifying 3 + 15t + -1t2 = 11 Solving 3 + 15t + -1t2 = 11 Solving for variable 't'. Reorder the terms: 3 + -11 + 15t + -1t2 = 11 + -11 Combine like terms: 3 + -11 = -8 -8 + 15t + -1t2 = 11 + -11 Combine like terms: 11 + -11 = 0 -8 + 15t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 8 + -15t + t2 = 0 Move the constant term to the right: Add '-8' to each side of the equation. 8 + -15t + -8 + t2 = 0 + -8 Reorder the terms: 8 + -8 + -15t + t2 = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -15t + t2 = 0 + -8 -15t + t2 = 0 + -8 Combine like terms: 0 + -8 = -8 -15t + t2 = -8 The t term is -15t. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15t + 56.25 + t2 = -8 + 56.25 Reorder the terms: 56.25 + -15t + t2 = -8 + 56.25 Combine like terms: -8 + 56.25 = 48.25 56.25 + -15t + t2 = 48.25 Factor a perfect square on the left side: (t + -7.5)(t + -7.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (t + -7.5) equal to 6.946221995 and -6.946221995.Subproblem 1
t + -7.5 = 6.946221995 Simplifying t + -7.5 = 6.946221995 Reorder the terms: -7.5 + t = 6.946221995 Solving -7.5 + t = 6.946221995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = 6.946221995 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = 6.946221995 + 7.5 t = 6.946221995 + 7.5 Combine like terms: 6.946221995 + 7.5 = 14.446221995 t = 14.446221995 Simplifying t = 14.446221995Subproblem 2
t + -7.5 = -6.946221995 Simplifying t + -7.5 = -6.946221995 Reorder the terms: -7.5 + t = -6.946221995 Solving -7.5 + t = -6.946221995 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + t = -6.946221995 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + t = -6.946221995 + 7.5 t = -6.946221995 + 7.5 Combine like terms: -6.946221995 + 7.5 = 0.553778005 t = 0.553778005 Simplifying t = 0.553778005Solution
The solution to the problem is based on the solutions from the subproblems. t = {14.446221995, 0.553778005}
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