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Simplifying t2 + 24t + -8 = 0 Reorder the terms: -8 + 24t + t2 = 0 Solving -8 + 24t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + 24t + 8 + t2 = 0 + 8 Reorder the terms: -8 + 8 + 24t + t2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 24t + t2 = 0 + 8 24t + t2 = 0 + 8 Combine like terms: 0 + 8 = 8 24t + t2 = 8 The t term is 24t. Take half its coefficient (12). Square it (144) and add it to both sides. Add '144' to each side of the equation. 24t + 144 + t2 = 8 + 144 Reorder the terms: 144 + 24t + t2 = 8 + 144 Combine like terms: 8 + 144 = 152 144 + 24t + t2 = 152 Factor a perfect square on the left side: (t + 12)(t + 12) = 152 Calculate the square root of the right side: 12.328828006 Break this problem into two subproblems by setting (t + 12) equal to 12.328828006 and -12.328828006.Subproblem 1
t + 12 = 12.328828006 Simplifying t + 12 = 12.328828006 Reorder the terms: 12 + t = 12.328828006 Solving 12 + t = 12.328828006 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + t = 12.328828006 + -12 Combine like terms: 12 + -12 = 0 0 + t = 12.328828006 + -12 t = 12.328828006 + -12 Combine like terms: 12.328828006 + -12 = 0.328828006 t = 0.328828006 Simplifying t = 0.328828006Subproblem 2
t + 12 = -12.328828006 Simplifying t + 12 = -12.328828006 Reorder the terms: 12 + t = -12.328828006 Solving 12 + t = -12.328828006 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-12' to each side of the equation. 12 + -12 + t = -12.328828006 + -12 Combine like terms: 12 + -12 = 0 0 + t = -12.328828006 + -12 t = -12.328828006 + -12 Combine like terms: -12.328828006 + -12 = -24.328828006 t = -24.328828006 Simplifying t = -24.328828006Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.328828006, -24.328828006}
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