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Simplifying 0 = 1.4 + 11t + -5t2 Solving 0 = 1.4 + 11t + -5t2 Solving for variable 't'. Combine like terms: 0 + -1.4 = -1.4 -1.4 + -11t + 5t2 = 1.4 + 11t + -5t2 + -1.4 + -11t + 5t2 Reorder the terms: -1.4 + -11t + 5t2 = 1.4 + -1.4 + 11t + -11t + -5t2 + 5t2 Combine like terms: 1.4 + -1.4 = 0.0 -1.4 + -11t + 5t2 = 0.0 + 11t + -11t + -5t2 + 5t2 -1.4 + -11t + 5t2 = 11t + -11t + -5t2 + 5t2 Combine like terms: 11t + -11t = 0 -1.4 + -11t + 5t2 = 0 + -5t2 + 5t2 -1.4 + -11t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -1.4 + -11t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.28 + -2.2t + t2 = 0 Move the constant term to the right: Add '0.28' to each side of the equation. -0.28 + -2.2t + 0.28 + t2 = 0 + 0.28 Reorder the terms: -0.28 + 0.28 + -2.2t + t2 = 0 + 0.28 Combine like terms: -0.28 + 0.28 = 0.00 0.00 + -2.2t + t2 = 0 + 0.28 -2.2t + t2 = 0 + 0.28 Combine like terms: 0 + 0.28 = 0.28 -2.2t + t2 = 0.28 The t term is -2.2t. Take half its coefficient (-1.1). Square it (1.21) and add it to both sides. Add '1.21' to each side of the equation. -2.2t + 1.21 + t2 = 0.28 + 1.21 Reorder the terms: 1.21 + -2.2t + t2 = 0.28 + 1.21 Combine like terms: 0.28 + 1.21 = 1.49 1.21 + -2.2t + t2 = 1.49 Factor a perfect square on the left side: (t + -1.1)(t + -1.1) = 1.49 Calculate the square root of the right side: 1.220655562 Break this problem into two subproblems by setting (t + -1.1) equal to 1.220655562 and -1.220655562.Subproblem 1
t + -1.1 = 1.220655562 Simplifying t + -1.1 = 1.220655562 Reorder the terms: -1.1 + t = 1.220655562 Solving -1.1 + t = 1.220655562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = 1.220655562 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = 1.220655562 + 1.1 t = 1.220655562 + 1.1 Combine like terms: 1.220655562 + 1.1 = 2.320655562 t = 2.320655562 Simplifying t = 2.320655562Subproblem 2
t + -1.1 = -1.220655562 Simplifying t + -1.1 = -1.220655562 Reorder the terms: -1.1 + t = -1.220655562 Solving -1.1 + t = -1.220655562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.1' to each side of the equation. -1.1 + 1.1 + t = -1.220655562 + 1.1 Combine like terms: -1.1 + 1.1 = 0.0 0.0 + t = -1.220655562 + 1.1 t = -1.220655562 + 1.1 Combine like terms: -1.220655562 + 1.1 = -0.120655562 t = -0.120655562 Simplifying t = -0.120655562Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.320655562, -0.120655562}
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