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Simplifying t2 + -100t = 21 Reorder the terms: -100t + t2 = 21 Solving -100t + t2 = 21 Solving for variable 't'. Reorder the terms: -21 + -100t + t2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -100t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -100t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + -100t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -100t + t2 = 0 + 21 -100t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 -100t + t2 = 21 The t term is -100t. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100t + 2500 + t2 = 21 + 2500 Reorder the terms: 2500 + -100t + t2 = 21 + 2500 Combine like terms: 21 + 2500 = 2521 2500 + -100t + t2 = 2521 Factor a perfect square on the left side: (t + -50)(t + -50) = 2521 Calculate the square root of the right side: 50.209560843 Break this problem into two subproblems by setting (t + -50) equal to 50.209560843 and -50.209560843.Subproblem 1
t + -50 = 50.209560843 Simplifying t + -50 = 50.209560843 Reorder the terms: -50 + t = 50.209560843 Solving -50 + t = 50.209560843 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = 50.209560843 + 50 Combine like terms: -50 + 50 = 0 0 + t = 50.209560843 + 50 t = 50.209560843 + 50 Combine like terms: 50.209560843 + 50 = 100.209560843 t = 100.209560843 Simplifying t = 100.209560843Subproblem 2
t + -50 = -50.209560843 Simplifying t + -50 = -50.209560843 Reorder the terms: -50 + t = -50.209560843 Solving -50 + t = -50.209560843 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + t = -50.209560843 + 50 Combine like terms: -50 + 50 = 0 0 + t = -50.209560843 + 50 t = -50.209560843 + 50 Combine like terms: -50.209560843 + 50 = -0.209560843 t = -0.209560843 Simplifying t = -0.209560843Solution
The solution to the problem is based on the solutions from the subproblems. t = {100.209560843, -0.209560843}
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