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Simplifying t2 + 32t + -23 = 0 Reorder the terms: -23 + 32t + t2 = 0 Solving -23 + 32t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + 32t + 23 + t2 = 0 + 23 Reorder the terms: -23 + 23 + 32t + t2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + 32t + t2 = 0 + 23 32t + t2 = 0 + 23 Combine like terms: 0 + 23 = 23 32t + t2 = 23 The t term is 32t. Take half its coefficient (16). Square it (256) and add it to both sides. Add '256' to each side of the equation. 32t + 256 + t2 = 23 + 256 Reorder the terms: 256 + 32t + t2 = 23 + 256 Combine like terms: 23 + 256 = 279 256 + 32t + t2 = 279 Factor a perfect square on the left side: (t + 16)(t + 16) = 279 Calculate the square root of the right side: 16.703293088 Break this problem into two subproblems by setting (t + 16) equal to 16.703293088 and -16.703293088.Subproblem 1
t + 16 = 16.703293088 Simplifying t + 16 = 16.703293088 Reorder the terms: 16 + t = 16.703293088 Solving 16 + t = 16.703293088 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + t = 16.703293088 + -16 Combine like terms: 16 + -16 = 0 0 + t = 16.703293088 + -16 t = 16.703293088 + -16 Combine like terms: 16.703293088 + -16 = 0.703293088 t = 0.703293088 Simplifying t = 0.703293088Subproblem 2
t + 16 = -16.703293088 Simplifying t + 16 = -16.703293088 Reorder the terms: 16 + t = -16.703293088 Solving 16 + t = -16.703293088 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-16' to each side of the equation. 16 + -16 + t = -16.703293088 + -16 Combine like terms: 16 + -16 = 0 0 + t = -16.703293088 + -16 t = -16.703293088 + -16 Combine like terms: -16.703293088 + -16 = -32.703293088 t = -32.703293088 Simplifying t = -32.703293088Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.703293088, -32.703293088}
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