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Simplifying t2 + 100t + -50 = 0 Reorder the terms: -50 + 100t + t2 = 0 Solving -50 + 100t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '50' to each side of the equation. -50 + 100t + 50 + t2 = 0 + 50 Reorder the terms: -50 + 50 + 100t + t2 = 0 + 50 Combine like terms: -50 + 50 = 0 0 + 100t + t2 = 0 + 50 100t + t2 = 0 + 50 Combine like terms: 0 + 50 = 50 100t + t2 = 50 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 = 50 + 2500 Reorder the terms: 2500 + 100t + t2 = 50 + 2500 Combine like terms: 50 + 2500 = 2550 2500 + 100t + t2 = 2550 Factor a perfect square on the left side: (t + 50)(t + 50) = 2550 Calculate the square root of the right side: 50.497524692 Break this problem into two subproblems by setting (t + 50) equal to 50.497524692 and -50.497524692.Subproblem 1
t + 50 = 50.497524692 Simplifying t + 50 = 50.497524692 Reorder the terms: 50 + t = 50.497524692 Solving 50 + t = 50.497524692 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 = 50.497524692 + -50 Combine like terms: 50 + -50 = 0 0 + t = 50.497524692 + -50 t = 50.497524692 + -50 Combine like terms: 50.497524692 + -50 = 0.497524692 t = 0.497524692 Simplifying t = 0.497524692Subproblem 2
t + 50 = -50.497524692 Simplifying t + 50 = -50.497524692 Reorder the terms: 50 + t = -50.497524692 Solving 50 + t = -50.497524692 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 = -50.497524692 + -50 Combine like terms: 50 + -50 = 0 0 + t = -50.497524692 + -50 t = -50.497524692 + -50 Combine like terms: -50.497524692 + -50 = -100.497524692 t = -100.497524692 Simplifying t = -100.497524692Solution
The solution to the problem is based on the solutions from the subproblems. t = {0.497524692, -100.497524692}
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