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Simplifying 55 = t2 + -1t Reorder the terms: 55 = -1t + t2 Solving 55 = -1t + t2 Solving for variable 't'. Reorder the terms: 55 + t + -1t2 = -1t + t + t2 + -1t2 Combine like terms: -1t + t = 0 55 + t + -1t2 = 0 + t2 + -1t2 55 + t + -1t2 = t2 + -1t2 Combine like terms: t2 + -1t2 = 0 55 + t + -1t2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -55 + -1t + t2 = 0 Move the constant term to the right: Add '55' to each side of the equation. -55 + -1t + 55 + t2 = 0 + 55 Reorder the terms: -55 + 55 + -1t + t2 = 0 + 55 Combine like terms: -55 + 55 = 0 0 + -1t + t2 = 0 + 55 -1t + t2 = 0 + 55 Combine like terms: 0 + 55 = 55 -1t + t2 = 55 The t term is t. 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 = 55 + 0.25 Reorder the terms: 0.25 + -1t + t2 = 55 + 0.25 Combine like terms: 55 + 0.25 = 55.25 0.25 + -1t + t2 = 55.25 Factor a perfect square on the left side: (t + 0.5)(t + 0.5) = 55.25 Calculate the square root of the right side: 7.433034374 Break this problem into two subproblems by setting (t + 0.5) equal to 7.433034374 and -7.433034374.Subproblem 1
t + 0.5 = 7.433034374 Simplifying t + 0.5 = 7.433034374 Reorder the terms: 0.5 + t = 7.433034374 Solving 0.5 + t = 7.433034374 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 = 7.433034374 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = 7.433034374 + -0.5 t = 7.433034374 + -0.5 Combine like terms: 7.433034374 + -0.5 = 6.933034374 t = 6.933034374 Simplifying t = 6.933034374Subproblem 2
t + 0.5 = -7.433034374 Simplifying t + 0.5 = -7.433034374 Reorder the terms: 0.5 + t = -7.433034374 Solving 0.5 + t = -7.433034374 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 = -7.433034374 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + t = -7.433034374 + -0.5 t = -7.433034374 + -0.5 Combine like terms: -7.433034374 + -0.5 = -7.933034374 t = -7.933034374 Simplifying t = -7.933034374Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.933034374, -7.933034374}
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