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Simplifying 3 = -5t2 + 45t + 4 Reorder the terms: 3 = 4 + 45t + -5t2 Solving 3 = 4 + 45t + -5t2 Solving for variable 't'. Combine like terms: 3 + -4 = -1 -1 + -45t + 5t2 = 4 + 45t + -5t2 + -4 + -45t + 5t2 Reorder the terms: -1 + -45t + 5t2 = 4 + -4 + 45t + -45t + -5t2 + 5t2 Combine like terms: 4 + -4 = 0 -1 + -45t + 5t2 = 0 + 45t + -45t + -5t2 + 5t2 -1 + -45t + 5t2 = 45t + -45t + -5t2 + 5t2 Combine like terms: 45t + -45t = 0 -1 + -45t + 5t2 = 0 + -5t2 + 5t2 -1 + -45t + 5t2 = -5t2 + 5t2 Combine like terms: -5t2 + 5t2 = 0 -1 + -45t + 5t2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -0.2 + -9t + t2 = 0 Move the constant term to the right: Add '0.2' to each side of the equation. -0.2 + -9t + 0.2 + t2 = 0 + 0.2 Reorder the terms: -0.2 + 0.2 + -9t + t2 = 0 + 0.2 Combine like terms: -0.2 + 0.2 = 0.0 0.0 + -9t + t2 = 0 + 0.2 -9t + t2 = 0 + 0.2 Combine like terms: 0 + 0.2 = 0.2 -9t + t2 = 0.2 The t term is -9t. Take half its coefficient (-4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. -9t + 20.25 + t2 = 0.2 + 20.25 Reorder the terms: 20.25 + -9t + t2 = 0.2 + 20.25 Combine like terms: 0.2 + 20.25 = 20.45 20.25 + -9t + t2 = 20.45 Factor a perfect square on the left side: (t + -4.5)(t + -4.5) = 20.45 Calculate the square root of the right side: 4.522167622 Break this problem into two subproblems by setting (t + -4.5) equal to 4.522167622 and -4.522167622.Subproblem 1
t + -4.5 = 4.522167622 Simplifying t + -4.5 = 4.522167622 Reorder the terms: -4.5 + t = 4.522167622 Solving -4.5 + t = 4.522167622 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = 4.522167622 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = 4.522167622 + 4.5 t = 4.522167622 + 4.5 Combine like terms: 4.522167622 + 4.5 = 9.022167622 t = 9.022167622 Simplifying t = 9.022167622Subproblem 2
t + -4.5 = -4.522167622 Simplifying t + -4.5 = -4.522167622 Reorder the terms: -4.5 + t = -4.522167622 Solving -4.5 + t = -4.522167622 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '4.5' to each side of the equation. -4.5 + 4.5 + t = -4.522167622 + 4.5 Combine like terms: -4.5 + 4.5 = 0.0 0.0 + t = -4.522167622 + 4.5 t = -4.522167622 + 4.5 Combine like terms: -4.522167622 + 4.5 = -0.022167622 t = -0.022167622 Simplifying t = -0.022167622Solution
The solution to the problem is based on the solutions from the subproblems. t = {9.022167622, -0.022167622}
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