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Simplifying t2 + 10t = 100 Reorder the terms: 10t + t2 = 100 Solving 10t + t2 = 100 Solving for variable 't'. Reorder the terms: -100 + 10t + t2 = 100 + -100 Combine like terms: 100 + -100 = 0 -100 + 10t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '100' to each side of the equation. -100 + 10t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + 10t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + 10t + t2 = 0 + 100 10t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 10t + t2 = 100 The t term is 10t. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10t + 25 + t2 = 100 + 25 Reorder the terms: 25 + 10t + t2 = 100 + 25 Combine like terms: 100 + 25 = 125 25 + 10t + t2 = 125 Factor a perfect square on the left side: (t + 5)(t + 5) = 125 Calculate the square root of the right side: 11.180339887 Break this problem into two subproblems by setting (t + 5) equal to 11.180339887 and -11.180339887.Subproblem 1
t + 5 = 11.180339887 Simplifying t + 5 = 11.180339887 Reorder the terms: 5 + t = 11.180339887 Solving 5 + t = 11.180339887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = 11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + t = 11.180339887 + -5 t = 11.180339887 + -5 Combine like terms: 11.180339887 + -5 = 6.180339887 t = 6.180339887 Simplifying t = 6.180339887Subproblem 2
t + 5 = -11.180339887 Simplifying t + 5 = -11.180339887 Reorder the terms: 5 + t = -11.180339887 Solving 5 + t = -11.180339887 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + t = -11.180339887 + -5 Combine like terms: 5 + -5 = 0 0 + t = -11.180339887 + -5 t = -11.180339887 + -5 Combine like terms: -11.180339887 + -5 = -16.180339887 t = -16.180339887 Simplifying t = -16.180339887Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.180339887, -16.180339887}
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