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Simplifying t * t + 2t + -48 = 14 Multiply t * t t2 + 2t + -48 = 14 Reorder the terms: -48 + 2t + t2 = 14 Solving -48 + 2t + t2 = 14 Solving for variable 't'. Reorder the terms: -48 + -14 + 2t + t2 = 14 + -14 Combine like terms: -48 + -14 = -62 -62 + 2t + t2 = 14 + -14 Combine like terms: 14 + -14 = 0 -62 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '62' to each side of the equation. -62 + 2t + 62 + t2 = 0 + 62 Reorder the terms: -62 + 62 + 2t + t2 = 0 + 62 Combine like terms: -62 + 62 = 0 0 + 2t + t2 = 0 + 62 2t + t2 = 0 + 62 Combine like terms: 0 + 62 = 62 2t + t2 = 62 The t term is 2t. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2t + 1 + t2 = 62 + 1 Reorder the terms: 1 + 2t + t2 = 62 + 1 Combine like terms: 62 + 1 = 63 1 + 2t + t2 = 63 Factor a perfect square on the left side: (t + 1)(t + 1) = 63 Calculate the square root of the right side: 7.937253933 Break this problem into two subproblems by setting (t + 1) equal to 7.937253933 and -7.937253933.Subproblem 1
t + 1 = 7.937253933 Simplifying t + 1 = 7.937253933 Reorder the terms: 1 + t = 7.937253933 Solving 1 + t = 7.937253933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = 7.937253933 + -1 Combine like terms: 1 + -1 = 0 0 + t = 7.937253933 + -1 t = 7.937253933 + -1 Combine like terms: 7.937253933 + -1 = 6.937253933 t = 6.937253933 Simplifying t = 6.937253933Subproblem 2
t + 1 = -7.937253933 Simplifying t + 1 = -7.937253933 Reorder the terms: 1 + t = -7.937253933 Solving 1 + t = -7.937253933 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + t = -7.937253933 + -1 Combine like terms: 1 + -1 = 0 0 + t = -7.937253933 + -1 t = -7.937253933 + -1 Combine like terms: -7.937253933 + -1 = -8.937253933 t = -8.937253933 Simplifying t = -8.937253933Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.937253933, -8.937253933}
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