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Simplifying -16t2 + 40t + 7 = 0 Reorder the terms: 7 + 40t + -16t2 = 0 Solving 7 + 40t + -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 + -2.5t + t2 = 0 Move the constant term to the right: Add '0.4375' to each side of the equation. -0.4375 + -2.5t + 0.4375 + t2 = 0 + 0.4375 Reorder the terms: -0.4375 + 0.4375 + -2.5t + t2 = 0 + 0.4375 Combine like terms: -0.4375 + 0.4375 = 0.0000 0.0000 + -2.5t + t2 = 0 + 0.4375 -2.5t + t2 = 0 + 0.4375 Combine like terms: 0 + 0.4375 = 0.4375 -2.5t + t2 = 0.4375 The t term is -2.5t. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5t + 1.5625 + t2 = 0.4375 + 1.5625 Reorder the terms: 1.5625 + -2.5t + t2 = 0.4375 + 1.5625 Combine like terms: 0.4375 + 1.5625 = 2 1.5625 + -2.5t + t2 = 2 Factor a perfect square on the left side: (t + -1.25)(t + -1.25) = 2 Calculate the square root of the right side: 1.414213562 Break this problem into two subproblems by setting (t + -1.25) equal to 1.414213562 and -1.414213562.Subproblem 1
t + -1.25 = 1.414213562 Simplifying t + -1.25 = 1.414213562 Reorder the terms: -1.25 + t = 1.414213562 Solving -1.25 + t = 1.414213562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = 1.414213562 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = 1.414213562 + 1.25 t = 1.414213562 + 1.25 Combine like terms: 1.414213562 + 1.25 = 2.664213562 t = 2.664213562 Simplifying t = 2.664213562Subproblem 2
t + -1.25 = -1.414213562 Simplifying t + -1.25 = -1.414213562 Reorder the terms: -1.25 + t = -1.414213562 Solving -1.25 + t = -1.414213562 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + t = -1.414213562 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + t = -1.414213562 + 1.25 t = -1.414213562 + 1.25 Combine like terms: -1.414213562 + 1.25 = -0.164213562 t = -0.164213562 Simplifying t = -0.164213562Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.664213562, -0.164213562}
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