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Simplifying t2 + -16t + 52 = 0 Reorder the terms: 52 + -16t + t2 = 0 Solving 52 + -16t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '-52' to each side of the equation. 52 + -16t + -52 + t2 = 0 + -52 Reorder the terms: 52 + -52 + -16t + t2 = 0 + -52 Combine like terms: 52 + -52 = 0 0 + -16t + t2 = 0 + -52 -16t + t2 = 0 + -52 Combine like terms: 0 + -52 = -52 -16t + t2 = -52 The t term is -16t. Take half its coefficient (-8). Square it (64) and add it to both sides. Add '64' to each side of the equation. -16t + 64 + t2 = -52 + 64 Reorder the terms: 64 + -16t + t2 = -52 + 64 Combine like terms: -52 + 64 = 12 64 + -16t + t2 = 12 Factor a perfect square on the left side: (t + -8)(t + -8) = 12 Calculate the square root of the right side: 3.464101615 Break this problem into two subproblems by setting (t + -8) equal to 3.464101615 and -3.464101615.Subproblem 1
t + -8 = 3.464101615 Simplifying t + -8 = 3.464101615 Reorder the terms: -8 + t = 3.464101615 Solving -8 + t = 3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = 3.464101615 + 8 Combine like terms: -8 + 8 = 0 0 + t = 3.464101615 + 8 t = 3.464101615 + 8 Combine like terms: 3.464101615 + 8 = 11.464101615 t = 11.464101615 Simplifying t = 11.464101615Subproblem 2
t + -8 = -3.464101615 Simplifying t + -8 = -3.464101615 Reorder the terms: -8 + t = -3.464101615 Solving -8 + t = -3.464101615 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '8' to each side of the equation. -8 + 8 + t = -3.464101615 + 8 Combine like terms: -8 + 8 = 0 0 + t = -3.464101615 + 8 t = -3.464101615 + 8 Combine like terms: -3.464101615 + 8 = 4.535898385 t = 4.535898385 Simplifying t = 4.535898385Solution
The solution to the problem is based on the solutions from the subproblems. t = {11.464101615, 4.535898385}
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