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Simplifying t2 + 20t + -100 = 0 Reorder the terms: -100 + 20t + t2 = 0 Solving -100 + 20t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 20t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + 20t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 20t + t2 = 0 + 100 20t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 20t + t2 = 100 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 = 100 + 100 Reorder the terms: 100 + 20t + t2 = 100 + 100 Combine like terms: 100 + 100 = 200 100 + 20t + t2 = 200 Factor a perfect square on the left side: (t + 10)(t + 10) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (t + 10) equal to 14.142135624 and -14.142135624.Subproblem 1
t + 10 = 14.142135624 Simplifying t + 10 = 14.142135624 Reorder the terms: 10 + t = 14.142135624 Solving 10 + t = 14.142135624 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 = 14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + t = 14.142135624 + -10 t = 14.142135624 + -10 Combine like terms: 14.142135624 + -10 = 4.142135624 t = 4.142135624 Simplifying t = 4.142135624Subproblem 2
t + 10 = -14.142135624 Simplifying t + 10 = -14.142135624 Reorder the terms: 10 + t = -14.142135624 Solving 10 + t = -14.142135624 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 = -14.142135624 + -10 Combine like terms: 10 + -10 = 0 0 + t = -14.142135624 + -10 t = -14.142135624 + -10 Combine like terms: -14.142135624 + -10 = -24.142135624 t = -24.142135624 Simplifying t = -24.142135624Solution
The solution to the problem is based on the solutions from the subproblems. t = {4.142135624, -24.142135624}
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