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Simplifying t2 + -6t + -100 = 0 Reorder the terms: -100 + -6t + t2 = 0 Solving -100 + -6t + 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 + -6t + 100 + t2 = 0 + 100 Reorder the terms: -100 + 100 + -6t + t2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -6t + t2 = 0 + 100 -6t + t2 = 0 + 100 Combine like terms: 0 + 100 = 100 -6t + t2 = 100 The t term is -6t. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6t + 9 + t2 = 100 + 9 Reorder the terms: 9 + -6t + t2 = 100 + 9 Combine like terms: 100 + 9 = 109 9 + -6t + t2 = 109 Factor a perfect square on the left side: (t + -3)(t + -3) = 109 Calculate the square root of the right side: 10.440306509 Break this problem into two subproblems by setting (t + -3) equal to 10.440306509 and -10.440306509.Subproblem 1
t + -3 = 10.440306509 Simplifying t + -3 = 10.440306509 Reorder the terms: -3 + t = 10.440306509 Solving -3 + t = 10.440306509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = 10.440306509 + 3 Combine like terms: -3 + 3 = 0 0 + t = 10.440306509 + 3 t = 10.440306509 + 3 Combine like terms: 10.440306509 + 3 = 13.440306509 t = 13.440306509 Simplifying t = 13.440306509Subproblem 2
t + -3 = -10.440306509 Simplifying t + -3 = -10.440306509 Reorder the terms: -3 + t = -10.440306509 Solving -3 + t = -10.440306509 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + t = -10.440306509 + 3 Combine like terms: -3 + 3 = 0 0 + t = -10.440306509 + 3 t = -10.440306509 + 3 Combine like terms: -10.440306509 + 3 = -7.440306509 t = -7.440306509 Simplifying t = -7.440306509Solution
The solution to the problem is based on the solutions from the subproblems. t = {13.440306509, -7.440306509}
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