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Simplifying -16t2 + 45t + 4 = 0 Reorder the terms: 4 + 45t + -16t2 = 0 Solving 4 + 45t + -16t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.25 + -2.8125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.8125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.8125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.8125t + t2 = 0 + 0.25 -2.8125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.8125t + t2 = 0.25 The t term is -2.8125t. Take half its coefficient (-1.40625). Square it (1.977539063) and add it to both sides. Add '1.977539063' to each side of the equation. -2.8125t + 1.977539063 + t2 = 0.25 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 0.25 + 1.977539063 Combine like terms: 0.25 + 1.977539063 = 2.227539063 1.977539063 + -2.8125t + t2 = 2.227539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 2.227539063 Calculate the square root of the right side: 1.492494242 Break this problem into two subproblems by setting (t + -1.40625) equal to 1.492494242 and -1.492494242.Subproblem 1
t + -1.40625 = 1.492494242 Simplifying t + -1.40625 = 1.492494242 Reorder the terms: -1.40625 + t = 1.492494242 Solving -1.40625 + t = 1.492494242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = 1.492494242 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.492494242 + 1.40625 t = 1.492494242 + 1.40625 Combine like terms: 1.492494242 + 1.40625 = 2.898744242 t = 2.898744242 Simplifying t = 2.898744242Subproblem 2
t + -1.40625 = -1.492494242 Simplifying t + -1.40625 = -1.492494242 Reorder the terms: -1.40625 + t = -1.492494242 Solving -1.40625 + t = -1.492494242 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.40625' to each side of the equation. -1.40625 + 1.40625 + t = -1.492494242 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.492494242 + 1.40625 t = -1.492494242 + 1.40625 Combine like terms: -1.492494242 + 1.40625 = -0.086244242 t = -0.086244242 Simplifying t = -0.086244242Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.898744242, -0.086244242}
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