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Simplifying -16t2 + 45t + 400 = 0 Reorder the terms: 400 + 45t + -16t2 = 0 Solving 400 + 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'. -25 + -2.8125t + t2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + -2.8125t + 25 + t2 = 0 + 25 Reorder the terms: -25 + 25 + -2.8125t + t2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + -2.8125t + t2 = 0 + 25 -2.8125t + t2 = 0 + 25 Combine like terms: 0 + 25 = 25 -2.8125t + t2 = 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 = 25 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 25 + 1.977539063 Combine like terms: 25 + 1.977539063 = 26.977539063 1.977539063 + -2.8125t + t2 = 26.977539063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 26.977539063 Calculate the square root of the right side: 5.193990668 Break this problem into two subproblems by setting (t + -1.40625) equal to 5.193990668 and -5.193990668.Subproblem 1
t + -1.40625 = 5.193990668 Simplifying t + -1.40625 = 5.193990668 Reorder the terms: -1.40625 + t = 5.193990668 Solving -1.40625 + t = 5.193990668 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 = 5.193990668 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 5.193990668 + 1.40625 t = 5.193990668 + 1.40625 Combine like terms: 5.193990668 + 1.40625 = 6.600240668 t = 6.600240668 Simplifying t = 6.600240668Subproblem 2
t + -1.40625 = -5.193990668 Simplifying t + -1.40625 = -5.193990668 Reorder the terms: -1.40625 + t = -5.193990668 Solving -1.40625 + t = -5.193990668 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 = -5.193990668 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -5.193990668 + 1.40625 t = -5.193990668 + 1.40625 Combine like terms: -5.193990668 + 1.40625 = -3.787740668 t = -3.787740668 Simplifying t = -3.787740668Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.600240668, -3.787740668}
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