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Simplifying 4 + 37t + -16t2 = 0 Solving 4 + 37t + -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 + -2.3125t + t2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -2.3125t + 0.25 + t2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -2.3125t + t2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -2.3125t + t2 = 0 + 0.25 -2.3125t + t2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -2.3125t + t2 = 0.25 The t term is -2.3125t. Take half its coefficient (-1.15625). Square it (1.336914063) and add it to both sides. Add '1.336914063' to each side of the equation. -2.3125t + 1.336914063 + t2 = 0.25 + 1.336914063 Reorder the terms: 1.336914063 + -2.3125t + t2 = 0.25 + 1.336914063 Combine like terms: 0.25 + 1.336914063 = 1.586914063 1.336914063 + -2.3125t + t2 = 1.586914063 Factor a perfect square on the left side: (t + -1.15625)(t + -1.15625) = 1.586914063 Calculate the square root of the right side: 1.259727773 Break this problem into two subproblems by setting (t + -1.15625) equal to 1.259727773 and -1.259727773.Subproblem 1
t + -1.15625 = 1.259727773 Simplifying t + -1.15625 = 1.259727773 Reorder the terms: -1.15625 + t = 1.259727773 Solving -1.15625 + t = 1.259727773 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + t = 1.259727773 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + t = 1.259727773 + 1.15625 t = 1.259727773 + 1.15625 Combine like terms: 1.259727773 + 1.15625 = 2.415977773 t = 2.415977773 Simplifying t = 2.415977773Subproblem 2
t + -1.15625 = -1.259727773 Simplifying t + -1.15625 = -1.259727773 Reorder the terms: -1.15625 + t = -1.259727773 Solving -1.15625 + t = -1.259727773 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '1.15625' to each side of the equation. -1.15625 + 1.15625 + t = -1.259727773 + 1.15625 Combine like terms: -1.15625 + 1.15625 = 0.00000 0.00000 + t = -1.259727773 + 1.15625 t = -1.259727773 + 1.15625 Combine like terms: -1.259727773 + 1.15625 = -0.103477773 t = -0.103477773 Simplifying t = -0.103477773Solution
The solution to the problem is based on the solutions from the subproblems. t = {2.415977773, -0.103477773}
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