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Simplifying 4t2 + 22t + -25 = 0 Reorder the terms: -25 + 22t + 4t2 = 0 Solving -25 + 22t + 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'. -6.25 + 5.5t + t2 = 0 Move the constant term to the right: Add '6.25' to each side of the equation. -6.25 + 5.5t + 6.25 + t2 = 0 + 6.25 Reorder the terms: -6.25 + 6.25 + 5.5t + t2 = 0 + 6.25 Combine like terms: -6.25 + 6.25 = 0.00 0.00 + 5.5t + t2 = 0 + 6.25 5.5t + t2 = 0 + 6.25 Combine like terms: 0 + 6.25 = 6.25 5.5t + t2 = 6.25 The t term is 5.5t. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5t + 7.5625 + t2 = 6.25 + 7.5625 Reorder the terms: 7.5625 + 5.5t + t2 = 6.25 + 7.5625 Combine like terms: 6.25 + 7.5625 = 13.8125 7.5625 + 5.5t + t2 = 13.8125 Factor a perfect square on the left side: (t + 2.75)(t + 2.75) = 13.8125 Calculate the square root of the right side: 3.716517187 Break this problem into two subproblems by setting (t + 2.75) equal to 3.716517187 and -3.716517187.Subproblem 1
t + 2.75 = 3.716517187 Simplifying t + 2.75 = 3.716517187 Reorder the terms: 2.75 + t = 3.716517187 Solving 2.75 + t = 3.716517187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = 3.716517187 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = 3.716517187 + -2.75 t = 3.716517187 + -2.75 Combine like terms: 3.716517187 + -2.75 = 0.966517187 t = 0.966517187 Simplifying t = 0.966517187Subproblem 2
t + 2.75 = -3.716517187 Simplifying t + 2.75 = -3.716517187 Reorder the terms: 2.75 + t = -3.716517187 Solving 2.75 + t = -3.716517187 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + t = -3.716517187 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + t = -3.716517187 + -2.75 t = -3.716517187 + -2.75 Combine like terms: -3.716517187 + -2.75 = -6.466517187 t = -6.466517187 Simplifying t = -6.466517187Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.966517187, -6.466517187}
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