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Simplifying 0 = -0.4t2 + 2.4t + 6.5 Reorder the terms: 0 = 6.5 + 2.4t + -0.4t2 Solving 0 = 6.5 + 2.4t + -0.4t2 Solving for variable 't'. Combine like terms: 0 + -6.5 = -6.5 -6.5 + -2.4t + 0.4t2 = 6.5 + 2.4t + -0.4t2 + -6.5 + -2.4t + 0.4t2 Reorder the terms: -6.5 + -2.4t + 0.4t2 = 6.5 + -6.5 + 2.4t + -2.4t + -0.4t2 + 0.4t2 Combine like terms: 6.5 + -6.5 = 0.0 -6.5 + -2.4t + 0.4t2 = 0.0 + 2.4t + -2.4t + -0.4t2 + 0.4t2 -6.5 + -2.4t + 0.4t2 = 2.4t + -2.4t + -0.4t2 + 0.4t2 Combine like terms: 2.4t + -2.4t = 0.0 -6.5 + -2.4t + 0.4t2 = 0.0 + -0.4t2 + 0.4t2 -6.5 + -2.4t + 0.4t2 = -0.4t2 + 0.4t2 Combine like terms: -0.4t2 + 0.4t2 = 0.0 -6.5 + -2.4t + 0.4t2 = 0.0 Begin completing the square. Divide all terms by 0.4 the coefficient of the squared term: Divide each side by '0.4'. -16.25 + -6t + t2 = 0 Move the constant term to the right: Add '16.25' to each side of the equation. -16.25 + -6t + 16.25 + t2 = 0 + 16.25 Reorder the terms: -16.25 + 16.25 + -6t + t2 = 0 + 16.25 Combine like terms: -16.25 + 16.25 = 0.00 0.00 + -6t + t2 = 0 + 16.25 -6t + t2 = 0 + 16.25 Combine like terms: 0 + 16.25 = 16.25 -6t + t2 = 16.25 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 16.25 + 9 Reorder the terms: 9 + -6t + t2 = 16.25 + 9 Combine like terms: 16.25 + 9 = 25.25 9 + -6t + t2 = 25.25 Factor a perfect square on the left side: (t + -3)(t + -3) = 25.25 Calculate the square root of the right side: 5.024937811 Break this problem into two subproblems by setting (t + -3) equal to 5.024937811 and -5.024937811.Subproblem 1
t + -3 = 5.024937811 Simplifying t + -3 = 5.024937811 Reorder the terms: -3 + t = 5.024937811 Solving -3 + t = 5.024937811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 5.024937811 + 3 Combine like terms: -3 + 3 = 0 0 + t = 5.024937811 + 3 t = 5.024937811 + 3 Combine like terms: 5.024937811 + 3 = 8.024937811 t = 8.024937811 Simplifying t = 8.024937811Subproblem 2
t + -3 = -5.024937811 Simplifying t + -3 = -5.024937811 Reorder the terms: -3 + t = -5.024937811 Solving -3 + t = -5.024937811 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -5.024937811 + 3 Combine like terms: -3 + 3 = 0 0 + t = -5.024937811 + 3 t = -5.024937811 + 3 Combine like terms: -5.024937811 + 3 = -2.024937811 t = -2.024937811 Simplifying t = -2.024937811Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.024937811, -2.024937811}
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