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Simplifying (4 + 6.25) * t2 + 4(4t) + 4(4) + -625 = 0 Combine like terms: 4 + 6.25 = 10.25 (10.25) * t2 + 4(4t) + 4(4) + -625 = 0 Remove parenthesis around (4t) 10.25t2 + 4 * 4t + 4(4) + -625 = 0 Multiply 4 * 4 10.25t2 + 16t + 4(4) + -625 = 0 Multiply 4 * 4 10.25t2 + 16t + 16 + -625 = 0 Reorder the terms: 16 + -625 + 16t + 10.25t2 = 0 Combine like terms: 16 + -625 = -609 -609 + 16t + 10.25t2 = 0 Solving -609 + 16t + 10.25t2 = 0 Solving for variable 't'. Begin completing the square. Divide all terms by 10.25 the coefficient of the squared term: Divide each side by '10.25'. -59.41463415 + 1.56097561t + t2 = 0 Move the constant term to the right: Add '59.41463415' to each side of the equation. -59.41463415 + 1.56097561t + 59.41463415 + t2 = 0 + 59.41463415 Reorder the terms: -59.41463415 + 59.41463415 + 1.56097561t + t2 = 0 + 59.41463415 Combine like terms: -59.41463415 + 59.41463415 = 0.00000000 0.00000000 + 1.56097561t + t2 = 0 + 59.41463415 1.56097561t + t2 = 0 + 59.41463415 Combine like terms: 0 + 59.41463415 = 59.41463415 1.56097561t + t2 = 59.41463415 The t term is 1.56097561t. Take half its coefficient (0.780487805). Square it (0.6091612138) and add it to both sides. Add '0.6091612138' to each side of the equation. 1.56097561t + 0.6091612138 + t2 = 59.41463415 + 0.6091612138 Reorder the terms: 0.6091612138 + 1.56097561t + t2 = 59.41463415 + 0.6091612138 Combine like terms: 59.41463415 + 0.6091612138 = 60.0237953638 0.6091612138 + 1.56097561t + t2 = 60.0237953638 Factor a perfect square on the left side: (t + 0.780487805)(t + 0.780487805) = 60.0237953638 Calculate the square root of the right side: 7.747502524 Break this problem into two subproblems by setting (t + 0.780487805) equal to 7.747502524 and -7.747502524.Subproblem 1
t + 0.780487805 = 7.747502524 Simplifying t + 0.780487805 = 7.747502524 Reorder the terms: 0.780487805 + t = 7.747502524 Solving 0.780487805 + t = 7.747502524 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.780487805' to each side of the equation. 0.780487805 + -0.780487805 + t = 7.747502524 + -0.780487805 Combine like terms: 0.780487805 + -0.780487805 = 0.000000000 0.000000000 + t = 7.747502524 + -0.780487805 t = 7.747502524 + -0.780487805 Combine like terms: 7.747502524 + -0.780487805 = 6.967014719 t = 6.967014719 Simplifying t = 6.967014719Subproblem 2
t + 0.780487805 = -7.747502524 Simplifying t + 0.780487805 = -7.747502524 Reorder the terms: 0.780487805 + t = -7.747502524 Solving 0.780487805 + t = -7.747502524 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-0.780487805' to each side of the equation. 0.780487805 + -0.780487805 + t = -7.747502524 + -0.780487805 Combine like terms: 0.780487805 + -0.780487805 = 0.000000000 0.000000000 + t = -7.747502524 + -0.780487805 t = -7.747502524 + -0.780487805 Combine like terms: -7.747502524 + -0.780487805 = -8.527990329 t = -8.527990329 Simplifying t = -8.527990329Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.967014719, -8.527990329}
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