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Simplifying -16t2 + 45t + 7 = 0 Reorder the terms: 7 + 45t + -16t2 = 0 Solving 7 + 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'. -0.4375 + -2.8125t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -2.8125t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -2.8125t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -2.8125t + t2 = 0 + 0.4375 -2.8125t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -2.8125t + t2 = 0.4375 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 = 0.4375 + 1.977539063 Reorder the terms: 1.977539063 + -2.8125t + t2 = 0.4375 + 1.977539063 Combine like terms: 0.4375 + 1.977539063 = 2.415039063 1.977539063 + -2.8125t + t2 = 2.415039063 Factor a perfect square on the left side: (t + -1.40625)(t + -1.40625) = 2.415039063 Calculate the square root of the right side: 1.554039595 Break this problem into two subproblems by setting (t + -1.40625) equal to 1.554039595 and -1.554039595.Subproblem 1
t + -1.40625 = 1.554039595 Simplifying t + -1.40625 = 1.554039595 Reorder the terms: -1.40625 + t = 1.554039595 Solving -1.40625 + t = 1.554039595 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 = 1.554039595 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = 1.554039595 + 1.40625 t = 1.554039595 + 1.40625 Combine like terms: 1.554039595 + 1.40625 = 2.960289595 t = 2.960289595 Simplifying t = 2.960289595Subproblem 2
t + -1.40625 = -1.554039595 Simplifying t + -1.40625 = -1.554039595 Reorder the terms: -1.40625 + t = -1.554039595 Solving -1.40625 + t = -1.554039595 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 = -1.554039595 + 1.40625 Combine like terms: -1.40625 + 1.40625 = 0.00000 0.00000 + t = -1.554039595 + 1.40625 t = -1.554039595 + 1.40625 Combine like terms: -1.554039595 + 1.40625 = -0.147789595 t = -0.147789595 Simplifying t = -0.147789595Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.960289595, -0.147789595}
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