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Simplifying 4 = 40 + 2t + -5t2 Solving 4 = 40 + 2t + -5t2 Solving for variable 't'. Combine like terms: 4 + -40 = -36 -36 + -2t + 5t2 = 40 + 2t + -5t2 + -40 + -2t + 5t2 Reorder the terms: -36 + -2t + 5t2 = 40 + -40 + 2t + -2t + -5t2 + 5t2 Combine like terms: 40 + -40 = 0 -36 + -2t + 5t2 = 0 + 2t + -2t + -5t2 + 5t2 -36 + -2t + 5t2 = 2t + -2t + -5t2 + 5t2 Combine like terms: 2t + -2t = 0 -36 + -2t + 5t2 = 0 + -5t2 + 5t2 -36 + -2t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -36 + -2t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -7.2 + -0.4t + t2 = 0 Move the constant term to the right: Add '7.2' to each side of the equation. -7.2 + -0.4t + 7.2 + t2 = 0 + 7.2 Reorder the terms: -7.2 + 7.2 + -0.4t + t2 = 0 + 7.2 Combine like terms: -7.2 + 7.2 = 0.0 0.0 + -0.4t + t2 = 0 + 7.2 -0.4t + t2 = 0 + 7.2 Combine like terms: 0 + 7.2 = 7.2 -0.4t + t2 = 7.2 The t term is -0.4t. Take half its coefficient (-0.2). Square it (0.04) and add it to both sides. Add '0.04' to each side of the equation. -0.4t + 0.04 + t2 = 7.2 + 0.04 Reorder the terms: 0.04 + -0.4t + t2 = 7.2 + 0.04 Combine like terms: 7.2 + 0.04 = 7.24 0.04 + -0.4t + t2 = 7.24 Factor a perfect square on the left side: (t + -0.2)(t + -0.2) = 7.24 Calculate the square root of the right side: 2.690724809 Break this problem into two subproblems by setting (t + -0.2) equal to 2.690724809 and -2.690724809.Subproblem 1
t + -0.2 = 2.690724809 Simplifying t + -0.2 = 2.690724809 Reorder the terms: -0.2 + t = 2.690724809 Solving -0.2 + t = 2.690724809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = 2.690724809 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = 2.690724809 + 0.2 t = 2.690724809 + 0.2 Combine like terms: 2.690724809 + 0.2 = 2.890724809 t = 2.890724809 Simplifying t = 2.890724809Subproblem 2
t + -0.2 = -2.690724809 Simplifying t + -0.2 = -2.690724809 Reorder the terms: -0.2 + t = -2.690724809 Solving -0.2 + t = -2.690724809 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.2' to each side of the equation. -0.2 + 0.2 + t = -2.690724809 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + t = -2.690724809 + 0.2 t = -2.690724809 + 0.2 Combine like terms: -2.690724809 + 0.2 = -2.490724809 t = -2.490724809 Simplifying t = -2.490724809Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.890724809, -2.490724809}
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