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Simplifying 36 = 0.3t2 + 0.3t Reorder the terms: 36 = 0.3t + 0.3t2 Solving 36 = 0.3t + 0.3t2 Solving for variable 't'. Reorder the terms: 36 + -0.3t + -0.3t2 = 0.3t + -0.3t + 0.3t2 + -0.3t2 Combine like terms: 0.3t + -0.3t = 0.0 36 + -0.3t + -0.3t2 = 0.0 + 0.3t2 + -0.3t2 36 + -0.3t + -0.3t2 = 0.3t2 + -0.3t2 Combine like terms: 0.3t2 + -0.3t2 = 0.0 36 + -0.3t + -0.3t2 = 0.0 Begin completing the square. Divide all terms by -0.3 the coefficient of the squared term: Divide each side by '-0.3'. -120 + t + t2 = 0 Move the constant term to the right: Add '120' to each side of the equation. -120 + t + 120 + t2 = 0 + 120 Reorder the terms: -120 + 120 + t + t2 = 0 + 120 Combine like terms: -120 + 120 = 0 0 + t + t2 = 0 + 120 t + t2 = 0 + 120 Combine like terms: 0 + 120 = 120 t + t2 = 120 The t term is t. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. + 0.25 + t2 = 120 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + t2 = 120 + 0.25 Combine like terms: 120 + 0.25 = 120.25 1.25 + t2 = 120.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 120.25 Calculate the square root of the right side: 10.9658561 Break this problem into two subproblems by setting (t + 0.5) equal to 10.9658561 and -10.9658561.Subproblem 1
t + 0.5 = 10.9658561 Simplifying t + 0.5 = 10.9658561 Reorder the terms: 0.5 + t = 10.9658561 Solving 0.5 + t = 10.9658561 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = 10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 10.9658561 + -0.5 t = 10.9658561 + -0.5 Combine like terms: 10.9658561 + -0.5 = 10.4658561 t = 10.4658561 Simplifying t = 10.4658561Subproblem 2
t + 0.5 = -10.9658561 Simplifying t + 0.5 = -10.9658561 Reorder the terms: 0.5 + t = -10.9658561 Solving 0.5 + t = -10.9658561 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + t = -10.9658561 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -10.9658561 + -0.5 t = -10.9658561 + -0.5 Combine like terms: -10.9658561 + -0.5 = -11.4658561 t = -11.4658561 Simplifying t = -11.4658561Solution
The solution to the problem is based on the solutions from the subproblems. t = {10.4658561, -11.4658561}
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