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Simplifying t2 + 28t + -192 = 0 Reorder the terms: -192 + 28t + t2 = 0 Solving -192 + 28t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '192' to each side of the equation. -192 + 28t + 192 + t2 = 0 + 192 Reorder the terms: -192 + 192 + 28t + t2 = 0 + 192 Combine like terms: -192 + 192 = 0 0 + 28t + t2 = 0 + 192 28t + t2 = 0 + 192 Combine like terms: 0 + 192 = 192 28t + t2 = 192 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 = 192 + 196 Reorder the terms: 196 + 28t + t2 = 192 + 196 Combine like terms: 192 + 196 = 388 196 + 28t + t2 = 388 Factor a perfect square on the left side: (t + 14)(t + 14) = 388 Calculate the square root of the right side: 19.697715604 Break this problem into two subproblems by setting (t + 14) equal to 19.697715604 and -19.697715604.Subproblem 1
t + 14 = 19.697715604 Simplifying t + 14 = 19.697715604 Reorder the terms: 14 + t = 19.697715604 Solving 14 + t = 19.697715604 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 = 19.697715604 + -14 Combine like terms: 14 + -14 = 0 0 + t = 19.697715604 + -14 t = 19.697715604 + -14 Combine like terms: 19.697715604 + -14 = 5.697715604 t = 5.697715604 Simplifying t = 5.697715604Subproblem 2
t + 14 = -19.697715604 Simplifying t + 14 = -19.697715604 Reorder the terms: 14 + t = -19.697715604 Solving 14 + t = -19.697715604 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 = -19.697715604 + -14 Combine like terms: 14 + -14 = 0 0 + t = -19.697715604 + -14 t = -19.697715604 + -14 Combine like terms: -19.697715604 + -14 = -33.697715604 t = -33.697715604 Simplifying t = -33.697715604Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.697715604, -33.697715604}
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