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Simplifying t2 + 12t + -90 = 0 Reorder the terms: -90 + 12t + t2 = 0 Solving -90 + 12t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '90' to each side of the equation. -90 + 12t + 90 + t2 = 0 + 90 Reorder the terms: -90 + 90 + 12t + t2 = 0 + 90 Combine like terms: -90 + 90 = 0 0 + 12t + t2 = 0 + 90 12t + t2 = 0 + 90 Combine like terms: 0 + 90 = 90 12t + t2 = 90 The t term is 12t. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12t + 36 + t2 = 90 + 36 Reorder the terms: 36 + 12t + t2 = 90 + 36 Combine like terms: 90 + 36 = 126 36 + 12t + t2 = 126 Factor a perfect square on the left side: (t + 6)(t + 6) = 126 Calculate the square root of the right side: 11.22497216 Break this problem into two subproblems by setting (t + 6) equal to 11.22497216 and -11.22497216.Subproblem 1
t + 6 = 11.22497216 Simplifying t + 6 = 11.22497216 Reorder the terms: 6 + t = 11.22497216 Solving 6 + t = 11.22497216 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = 11.22497216 + -6 Combine like terms: 6 + -6 = 0 0 + t = 11.22497216 + -6 t = 11.22497216 + -6 Combine like terms: 11.22497216 + -6 = 5.22497216 t = 5.22497216 Simplifying t = 5.22497216Subproblem 2
t + 6 = -11.22497216 Simplifying t + 6 = -11.22497216 Reorder the terms: 6 + t = -11.22497216 Solving 6 + t = -11.22497216 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + t = -11.22497216 + -6 Combine like terms: 6 + -6 = 0 0 + t = -11.22497216 + -6 t = -11.22497216 + -6 Combine like terms: -11.22497216 + -6 = -17.22497216 t = -17.22497216 Simplifying t = -17.22497216Solution
The solution to the problem is based on the solutions from the subproblems. t = {5.22497216, -17.22497216}
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