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Simplifying 6 = -0.5t2 + 6t + -9 Reorder the terms: 6 = -9 + 6t + -0.5t2 Solving 6 = -9 + 6t + -0.5t2 Solving for variable 't'. Combine like terms: 6 + 9 = 15 15 + -6t + 0.5t2 = -9 + 6t + -0.5t2 + 9 + -6t + 0.5t2 Reorder the terms: 15 + -6t + 0.5t2 = -9 + 9 + 6t + -6t + -0.5t2 + 0.5t2 Combine like terms: -9 + 9 = 0 15 + -6t + 0.5t2 = 0 + 6t + -6t + -0.5t2 + 0.5t2 15 + -6t + 0.5t2 = 6t + -6t + -0.5t2 + 0.5t2 Combine like terms: 6t + -6t = 0 15 + -6t + 0.5t2 = 0 + -0.5t2 + 0.5t2 15 + -6t + 0.5t2 = -0.5t2 + 0.5t2 Combine like terms: -0.5t2 + 0.5t2 = 0.0 15 + -6t + 0.5t2 = 0.0 Begin completing the square. Divide all terms by 0.5 the coefficient of the squared term: Divide each side by '0.5'. 30 + -12t + t2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -12t + -30 + t2 = 0 + -30 Reorder the terms: 30 + -30 + -12t + t2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -12t + t2 = 0 + -30 -12t + t2 = 0 + -30 Combine like terms: 0 + -30 = -30 -12t + t2 = -30 The t term is -12t. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12t + 36 + t2 = -30 + 36 Reorder the terms: 36 + -12t + t2 = -30 + 36 Combine like terms: -30 + 36 = 6 36 + -12t + t2 = 6 Factor a perfect square on the left side: (t + -6)(t + -6) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (t + -6) equal to 2.449489743 and -2.449489743.Subproblem 1
t + -6 = 2.449489743 Simplifying t + -6 = 2.449489743 Reorder the terms: -6 + t = 2.449489743 Solving -6 + t = 2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = 2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + t = 2.449489743 + 6 t = 2.449489743 + 6 Combine like terms: 2.449489743 + 6 = 8.449489743 t = 8.449489743 Simplifying t = 8.449489743Subproblem 2
t + -6 = -2.449489743 Simplifying t + -6 = -2.449489743 Reorder the terms: -6 + t = -2.449489743 Solving -6 + t = -2.449489743 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + t = -2.449489743 + 6 Combine like terms: -6 + 6 = 0 0 + t = -2.449489743 + 6 t = -2.449489743 + 6 Combine like terms: -2.449489743 + 6 = 3.550510257 t = 3.550510257 Simplifying t = 3.550510257Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.449489743, 3.550510257}
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