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Simplifying 0 = 4t2 + -5t + -25 Reorder the terms: 0 = -25 + -5t + 4t2 Solving 0 = -25 + -5t + 4t2 Solving for variable 't'. Combine like terms: 0 + 25 = 25 25 + 5t + -4t2 = -25 + -5t + 4t2 + 25 + 5t + -4t2 Reorder the terms: 25 + 5t + -4t2 = -25 + 25 + -5t + 5t + 4t2 + -4t2 Combine like terms: -25 + 25 = 0 25 + 5t + -4t2 = 0 + -5t + 5t + 4t2 + -4t2 25 + 5t + -4t2 = -5t + 5t + 4t2 + -4t2 Combine like terms: -5t + 5t = 0 25 + 5t + -4t2 = 0 + 4t2 + -4t2 25 + 5t + -4t2 = 4t2 + -4t2 Combine like terms: 4t2 + -4t2 = 0 25 + 5t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -6.25 + -1.25t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + -1.25t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + -1.25t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + -1.25t + t2 = 0 + 6.25 -1.25t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 -1.25t + t2 = 6.25 The t term is -1.25t. Take half its coefficient (-0.625). Square it (0.390625) and add it to both sides. Add '0.390625' to each side of the equation. -1.25t + 0.390625 + t2 = 6.25 + 0.390625 Reorder the terms: 0.390625 + -1.25t + t2 = 6.25 + 0.390625 Combine like terms: 6.25 + 0.390625 = 6.640625 0.390625 + -1.25t + t2 = 6.640625 Factor a perfect square on the left side: (t + -0.625)(t + -0.625) = 6.640625 Calculate the square root of the right side: 2.576941016 Break this problem into two subproblems by setting (t + -0.625) equal to 2.576941016 and -2.576941016.Subproblem 1
t + -0.625 = 2.576941016 Simplifying t + -0.625 = 2.576941016 Reorder the terms: -0.625 + t = 2.576941016 Solving -0.625 + t = 2.576941016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = 2.576941016 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = 2.576941016 + 0.625 t = 2.576941016 + 0.625 Combine like terms: 2.576941016 + 0.625 = 3.201941016 t = 3.201941016 Simplifying t = 3.201941016Subproblem 2
t + -0.625 = -2.576941016 Simplifying t + -0.625 = -2.576941016 Reorder the terms: -0.625 + t = -2.576941016 Solving -0.625 + t = -2.576941016 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '0.625' to each side of the equation. -0.625 + 0.625 + t = -2.576941016 + 0.625 Combine like terms: -0.625 + 0.625 = 0.000 0.000 + t = -2.576941016 + 0.625 t = -2.576941016 + 0.625 Combine like terms: -2.576941016 + 0.625 = -1.951941016 t = -1.951941016 Simplifying t = -1.951941016Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.201941016, -1.951941016}
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