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Simplifying t2 + -63 = -14t Reorder the terms: -63 + t2 = -14t Solving -63 + t2 = -14t Solving for variable 't'. Reorder the terms: -63 + 14t + t2 = -14t + 14t Combine like terms: -14t + 14t = 0 -63 + 14t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '63' to each side of the equation. -63 + 14t + 63 + t2 = 0 + 63 Reorder the terms: -63 + 63 + 14t + t2 = 0 + 63 Combine like terms: -63 + 63 = 0 0 + 14t + t2 = 0 + 63 14t + t2 = 0 + 63 Combine like terms: 0 + 63 = 63 14t + t2 = 63 The t term is 14t. Take half its coefficient (7). Square it (49) and add it to both sides. Add '49' to each side of the equation. 14t + 49 + t2 = 63 + 49 Reorder the terms: 49 + 14t + t2 = 63 + 49 Combine like terms: 63 + 49 = 112 49 + 14t + t2 = 112 Factor a perfect square on the left side: (t + 7)(t + 7) = 112 Calculate the square root of the right side: 10.583005244 Break this problem into two subproblems by setting (t + 7) equal to 10.583005244 and -10.583005244.Subproblem 1
t + 7 = 10.583005244 Simplifying t + 7 = 10.583005244 Reorder the terms: 7 + t = 10.583005244 Solving 7 + t = 10.583005244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = 10.583005244 + -7 Combine like terms: 7 + -7 = 0 0 + t = 10.583005244 + -7 t = 10.583005244 + -7 Combine like terms: 10.583005244 + -7 = 3.583005244 t = 3.583005244 Simplifying t = 3.583005244Subproblem 2
t + 7 = -10.583005244 Simplifying t + 7 = -10.583005244 Reorder the terms: 7 + t = -10.583005244 Solving 7 + t = -10.583005244 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + t = -10.583005244 + -7 Combine like terms: 7 + -7 = 0 0 + t = -10.583005244 + -7 t = -10.583005244 + -7 Combine like terms: -10.583005244 + -7 = -17.583005244 t = -17.583005244 Simplifying t = -17.583005244Solution
The solution to the problem is based on the solutions from the subproblems. t = {3.583005244, -17.583005244}
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