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Simplifying t2 + 16t = -33 Reorder the terms: 16t + t2 = -33 Solving 16t + t2 = -33 Solving for variable 't'. Reorder the terms: 33 + 16t + t2 = -33 + 33 Combine like terms: -33 + 33 = 0 33 + 16t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-33' to each side of the equation. 33 + 16t + -33 + t2 = 0 + -33 Reorder the terms: 33 + -33 + 16t + t2 = 0 + -33 Combine like terms: 33 + -33 = 0 0 + 16t + t2 = 0 + -33 16t + t2 = 0 + -33 Combine like terms: 0 + -33 = -33 16t + t2 = -33 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 = -33 + 64 Reorder the terms: 64 + 16t + t2 = -33 + 64 Combine like terms: -33 + 64 = 31 64 + 16t + t2 = 31 Factor a perfect square on the left side: (t + 8)(t + 8) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (t + 8) equal to 5.567764363 and -5.567764363.Subproblem 1
t + 8 = 5.567764363 Simplifying t + 8 = 5.567764363 Reorder the terms: 8 + t = 5.567764363 Solving 8 + t = 5.567764363 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 = 5.567764363 + -8 Combine like terms: 8 + -8 = 0 0 + t = 5.567764363 + -8 t = 5.567764363 + -8 Combine like terms: 5.567764363 + -8 = -2.432235637 t = -2.432235637 Simplifying t = -2.432235637Subproblem 2
t + 8 = -5.567764363 Simplifying t + 8 = -5.567764363 Reorder the terms: 8 + t = -5.567764363 Solving 8 + t = -5.567764363 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 = -5.567764363 + -8 Combine like terms: 8 + -8 = 0 0 + t = -5.567764363 + -8 t = -5.567764363 + -8 Combine like terms: -5.567764363 + -8 = -13.567764363 t = -13.567764363 Simplifying t = -13.567764363Solution
The solution to the problem is based on the solutions from the subproblems. t = {-2.432235637, -13.567764363}
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