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Simplifying 6.61 = 11.5t + -5t2 Solving 6.61 = 11.5t + -5t2 Solving for variable 't'. Reorder the terms: 6.61 + -11.5t + 5t2 = 11.5t + -11.5t + -5t2 + 5t2 Combine like terms: 11.5t + -11.5t = 0.0 6.61 + -11.5t + 5t2 = 0.0 + -5t2 + 5t2 6.61 + -11.5t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 6.61 + -11.5t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 1.322 + -2.3t + t2 = 0 Move the constant term to the right: Add '-1.322' to each side of the equation. 1.322 + -2.3t + -1.322 + t2 = 0 + -1.322 Reorder the terms: 1.322 + -1.322 + -2.3t + t2 = 0 + -1.322 Combine like terms: 1.322 + -1.322 = 0.000 0.000 + -2.3t + t2 = 0 + -1.322 -2.3t + t2 = 0 + -1.322 Combine like terms: 0 + -1.322 = -1.322 -2.3t + t2 = -1.322 The t term is -2.3t. Take half its coefficient (-1.15). Square it (1.3225) and add it to both sides. Add '1.3225' to each side of the equation. -2.3t + 1.3225 + t2 = -1.322 + 1.3225 Reorder the terms: 1.3225 + -2.3t + t2 = -1.322 + 1.3225 Combine like terms: -1.322 + 1.3225 = 0.0005 1.3225 + -2.3t + t2 = 0.0005 Factor a perfect square on the left side: (t + -1.15)(t + -1.15) = 0.0005 Calculate the square root of the right side: 0.02236068 Break this problem into two subproblems by setting (t + -1.15) equal to 0.02236068 and -0.02236068.Subproblem 1
t + -1.15 = 0.02236068 Simplifying t + -1.15 = 0.02236068 Reorder the terms: -1.15 + t = 0.02236068 Solving -1.15 + t = 0.02236068 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + t = 0.02236068 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + t = 0.02236068 + 1.15 t = 0.02236068 + 1.15 Combine like terms: 0.02236068 + 1.15 = 1.17236068 t = 1.17236068 Simplifying t = 1.17236068Subproblem 2
t + -1.15 = -0.02236068 Simplifying t + -1.15 = -0.02236068 Reorder the terms: -1.15 + t = -0.02236068 Solving -1.15 + t = -0.02236068 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15' to each side of the equation. -1.15 + 1.15 + t = -0.02236068 + 1.15 Combine like terms: -1.15 + 1.15 = 0.00 0.00 + t = -0.02236068 + 1.15 t = -0.02236068 + 1.15 Combine like terms: -0.02236068 + 1.15 = 1.12763932 t = 1.12763932 Simplifying t = 1.12763932Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.17236068, 1.12763932}
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