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Simplifying t2 + 28t + -3 = 0 Reorder the terms: -3 + 28t + t2 = 0 Solving -3 + 28t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '3' to each side of the equation. -3 + 28t + 3 + t2 = 0 + 3 Reorder the terms: -3 + 3 + 28t + t2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 28t + t2 = 0 + 3 28t + t2 = 0 + 3 Combine like terms: 0 + 3 = 3 28t + t2 = 3 The t term is 28t. Take half its coefficient (14). Square it (196) and add it to both sides. Add '196' to each side of the equation. 28t + 196 + t2 = 3 + 196 Reorder the terms: 196 + 28t + t2 = 3 + 196 Combine like terms: 3 + 196 = 199 196 + 28t + t2 = 199 Factor a perfect square on the left side: (t + 14)(t + 14) = 199 Calculate the square root of the right side: 14.10673598 Break this problem into two subproblems by setting (t + 14) equal to 14.10673598 and -14.10673598.Subproblem 1
t + 14 = 14.10673598 Simplifying t + 14 = 14.10673598 Reorder the terms: 14 + t = 14.10673598 Solving 14 + t = 14.10673598 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + t = 14.10673598 + -14 Combine like terms: 14 + -14 = 0 0 + t = 14.10673598 + -14 t = 14.10673598 + -14 Combine like terms: 14.10673598 + -14 = 0.10673598 t = 0.10673598 Simplifying t = 0.10673598Subproblem 2
t + 14 = -14.10673598 Simplifying t + 14 = -14.10673598 Reorder the terms: 14 + t = -14.10673598 Solving 14 + t = -14.10673598 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-14' to each side of the equation. 14 + -14 + t = -14.10673598 + -14 Combine like terms: 14 + -14 = 0 0 + t = -14.10673598 + -14 t = -14.10673598 + -14 Combine like terms: -14.10673598 + -14 = -28.10673598 t = -28.10673598 Simplifying t = -28.10673598Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.10673598, -28.10673598}
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