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Simplifying t2 + 20t + 25 = 0 Reorder the terms: 25 + 20t + t2 = 0 Solving 25 + 20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-25' to each side of the equation. 25 + 20t + -25 + t2 = 0 + -25 Reorder the terms: 25 + -25 + 20t + t2 = 0 + -25 Combine like terms: 25 + -25 = 0 0 + 20t + t2 = 0 + -25 20t + t2 = 0 + -25 Combine like terms: 0 + -25 = -25 20t + t2 = -25 The t term is 20t. Take half its coefficient (10). Square it (100) and add it to both sides. Add '100' to each side of the equation. 20t + 100 + t2 = -25 + 100 Reorder the terms: 100 + 20t + t2 = -25 + 100 Combine like terms: -25 + 100 = 75 100 + 20t + t2 = 75 Factor a perfect square on the left side: (t + 10)(t + 10) = 75 Calculate the square root of the right side: 8.660254038 Break this problem into two subproblems by setting (t + 10) equal to 8.660254038 and -8.660254038.Subproblem 1
t + 10 = 8.660254038 Simplifying t + 10 = 8.660254038 Reorder the terms: 10 + t = 8.660254038 Solving 10 + t = 8.660254038 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = 8.660254038 + -10 Combine like terms: 10 + -10 = 0 0 + t = 8.660254038 + -10 t = 8.660254038 + -10 Combine like terms: 8.660254038 + -10 = -1.339745962 t = -1.339745962 Simplifying t = -1.339745962Subproblem 2
t + 10 = -8.660254038 Simplifying t + 10 = -8.660254038 Reorder the terms: 10 + t = -8.660254038 Solving 10 + t = -8.660254038 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-10' to each side of the equation. 10 + -10 + t = -8.660254038 + -10 Combine like terms: 10 + -10 = 0 0 + t = -8.660254038 + -10 t = -8.660254038 + -10 Combine like terms: -8.660254038 + -10 = -18.660254038 t = -18.660254038 Simplifying t = -18.660254038Solution
The solution to the problem is based on the solutions from the subproblems. t = {-1.339745962, -18.660254038}
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