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Simplifying t * t + 2t + -48 = 12 Multiply t * t t2 + 2t + -48 = 12 Reorder the terms: -48 + 2t + t2 = 12 Solving -48 + 2t + t2 = 12 Solving for variable 't'. Reorder the terms: -48 + -12 + 2t + t2 = 12 + -12 Combine like terms: -48 + -12 = -60 -60 + 2t + t2 = 12 + -12 Combine like terms: 12 + -12 = 0 -60 + 2t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 2t + 60 + t2 = 0 + 60 Reorder the terms: -60 + 60 + 2t + t2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 2t + t2 = 0 + 60 2t + t2 = 0 + 60 Combine like terms: 0 + 60 = 60 2t + t2 = 60 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 = 60 + 1 Reorder the terms: 1 + 2t + t2 = 60 + 1 Combine like terms: 60 + 1 = 61 1 + 2t + t2 = 61 Factor a perfect square on the left side: (t + 1)(t + 1) = 61 Calculate the square root of the right side: 7.810249676 Break this problem into two subproblems by setting (t + 1) equal to 7.810249676 and -7.810249676.Subproblem 1
t + 1 = 7.810249676 Simplifying t + 1 = 7.810249676 Reorder the terms: 1 + t = 7.810249676 Solving 1 + t = 7.810249676 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 = 7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + t = 7.810249676 + -1 t = 7.810249676 + -1 Combine like terms: 7.810249676 + -1 = 6.810249676 t = 6.810249676 Simplifying t = 6.810249676Subproblem 2
t + 1 = -7.810249676 Simplifying t + 1 = -7.810249676 Reorder the terms: 1 + t = -7.810249676 Solving 1 + t = -7.810249676 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 = -7.810249676 + -1 Combine like terms: 1 + -1 = 0 0 + t = -7.810249676 + -1 t = -7.810249676 + -1 Combine like terms: -7.810249676 + -1 = -8.810249676 t = -8.810249676 Simplifying t = -8.810249676Solution
The solution to the problem is based on the solutions from the subproblems. t = {6.810249676, -8.810249676}
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