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Simplifying 5t = 5t2 + -24 Reorder the terms: 5t = -24 + 5t2 Solving 5t = -24 + 5t2 Solving for variable 't'. Reorder the terms: 24 + 5t + -5t2 = -24 + 5t2 + 24 + -5t2 Reorder the terms: 24 + 5t + -5t2 = -24 + 24 + 5t2 + -5t2 Combine like terms: -24 + 24 = 0 24 + 5t + -5t2 = 0 + 5t2 + -5t2 24 + 5t + -5t2 = 5t2 + -5t2 Combine like terms: 5t2 + -5t2 = 0 24 + 5t + -5t2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. -4.8 + -1t + t2 = 0 Move the constant term to the right: Add '4.8' to each side of the equation. -4.8 + -1t + 4.8 + t2 = 0 + 4.8 Reorder the terms: -4.8 + 4.8 + -1t + t2 = 0 + 4.8 Combine like terms: -4.8 + 4.8 = 0.0 0.0 + -1t + t2 = 0 + 4.8 -1t + t2 = 0 + 4.8 Combine like terms: 0 + 4.8 = 4.8 -1t + t2 = 4.8 The t term is -1t. 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. -1t + 0.25 + t2 = 4.8 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 4.8 + 0.25 Combine like terms: 4.8 + 0.25 = 5.05 0.25 + -1t + t2 = 5.05 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 5.05 Calculate the square root of the right side: 2.247220505 Break this problem into two subproblems by setting (t + -0.5) equal to 2.247220505 and -2.247220505.Subproblem 1
t + -0.5 = 2.247220505 Simplifying t + -0.5 = 2.247220505 Reorder the terms: -0.5 + t = 2.247220505 Solving -0.5 + t = 2.247220505 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 = 2.247220505 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 2.247220505 + 0.5 t = 2.247220505 + 0.5 Combine like terms: 2.247220505 + 0.5 = 2.747220505 t = 2.747220505 Simplifying t = 2.747220505Subproblem 2
t + -0.5 = -2.247220505 Simplifying t + -0.5 = -2.247220505 Reorder the terms: -0.5 + t = -2.247220505 Solving -0.5 + t = -2.247220505 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 = -2.247220505 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -2.247220505 + 0.5 t = -2.247220505 + 0.5 Combine like terms: -2.247220505 + 0.5 = -1.747220505 t = -1.747220505 Simplifying t = -1.747220505Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.747220505, -1.747220505}
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