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Simplifying 440 = 16t2 + 4t Reorder the terms: 440 = 4t + 16t2 Solving 440 = 4t + 16t2 Solving for variable 't'. Reorder the terms: 440 + -4t + -16t2 = 4t + -4t + 16t2 + -16t2 Combine like terms: 4t + -4t = 0 440 + -4t + -16t2 = 0 + 16t2 + -16t2 440 + -4t + -16t2 = 16t2 + -16t2 Combine like terms: 16t2 + -16t2 = 0 440 + -4t + -16t2 = 0 Factor out the Greatest Common Factor (GCF), '4'. 4(110 + -1t + -4t2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(110 + -1t + -4t2)' equal to zero and attempt to solve: Simplifying 110 + -1t + -4t2 = 0 Solving 110 + -1t + -4t2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -27.5 + 0.25t + t2 = 0 Move the constant term to the right: Add '27.5' to each side of the equation. -27.5 + 0.25t + 27.5 + t2 = 0 + 27.5 Reorder the terms: -27.5 + 27.5 + 0.25t + t2 = 0 + 27.5 Combine like terms: -27.5 + 27.5 = 0.0 0.0 + 0.25t + t2 = 0 + 27.5 0.25t + t2 = 0 + 27.5 Combine like terms: 0 + 27.5 = 27.5 0.25t + t2 = 27.5 The t term is 0.25t. Take half its coefficient (0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. 0.25t + 0.015625 + t2 = 27.5 + 0.015625 Reorder the terms: 0.015625 + 0.25t + t2 = 27.5 + 0.015625 Combine like terms: 27.5 + 0.015625 = 27.515625 0.015625 + 0.25t + t2 = 27.515625 Factor a perfect square on the left side: (t + 0.125)(t + 0.125) = 27.515625 Calculate the square root of the right side: 5.245533815 Break this problem into two subproblems by setting (t + 0.125) equal to 5.245533815 and -5.245533815.Subproblem 1
t + 0.125 = 5.245533815 Simplifying t + 0.125 = 5.245533815 Reorder the terms: 0.125 + t = 5.245533815 Solving 0.125 + t = 5.245533815 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = 5.245533815 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = 5.245533815 + -0.125 t = 5.245533815 + -0.125 Combine like terms: 5.245533815 + -0.125 = 5.120533815 t = 5.120533815 Simplifying t = 5.120533815Subproblem 2
t + 0.125 = -5.245533815 Simplifying t + 0.125 = -5.245533815 Reorder the terms: 0.125 + t = -5.245533815 Solving 0.125 + t = -5.245533815 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.125' to each side of the equation. 0.125 + -0.125 + t = -5.245533815 + -0.125 Combine like terms: 0.125 + -0.125 = 0.000 0.000 + t = -5.245533815 + -0.125 t = -5.245533815 + -0.125 Combine like terms: -5.245533815 + -0.125 = -5.370533815 t = -5.370533815 Simplifying t = -5.370533815Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.120533815, -5.370533815}Solution
t = {5.120533815, -5.370533815}
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