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Simplifying 4t2 + -4t + -5 = 0 Reorder the terms: -5 + -4t + 4t2 = 0 Solving -5 + -4t + 4t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.25 + -1t + t2 = 0 Move the constant term to the right: Add '1.25' to each side of the equation. -1.25 + -1t + 1.25 + t2 = 0 + 1.25 Reorder the terms: -1.25 + 1.25 + -1t + t2 = 0 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + -1t + t2 = 0 + 1.25 -1t + t2 = 0 + 1.25 Combine like terms: 0 + 1.25 = 1.25 -1t + t2 = 1.25 The t term is -1t. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1t + 0.25 + t2 = 1.25 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 1.25 + 0.25 Combine like terms: 1.25 + 0.25 = 1.5 0.25 + -1t + t2 = 1.5 Factor a perfect square on the left side: (t + -0.5)(t + -0.5) = 1.5 Calculate the square root of the right side: 1.224744871 Break this problem into two subproblems by setting (t + -0.5) equal to 1.224744871 and -1.224744871.Subproblem 1
t + -0.5 = 1.224744871 Simplifying t + -0.5 = 1.224744871 Reorder the terms: -0.5 + t = 1.224744871 Solving -0.5 + t = 1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = 1.224744871 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = 1.224744871 + 0.5 t = 1.224744871 + 0.5 Combine like terms: 1.224744871 + 0.5 = 1.724744871 t = 1.724744871 Simplifying t = 1.724744871Subproblem 2
t + -0.5 = -1.224744871 Simplifying t + -0.5 = -1.224744871 Reorder the terms: -0.5 + t = -1.224744871 Solving -0.5 + t = -1.224744871 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + t = -1.224744871 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + t = -1.224744871 + 0.5 t = -1.224744871 + 0.5 Combine like terms: -1.224744871 + 0.5 = -0.724744871 t = -0.724744871 Simplifying t = -0.724744871Solution
The solution to the problem is based on the solutions from the subproblems. t = {1.724744871, -0.724744871}
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