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Simplifying t2 + -40t + -64 = 0 Reorder the terms: -64 + -40t + t2 = 0 Solving -64 + -40t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '64' to each side of the equation. -64 + -40t + 64 + t2 = 0 + 64 Reorder the terms: -64 + 64 + -40t + t2 = 0 + 64 Combine like terms: -64 + 64 = 0 0 + -40t + t2 = 0 + 64 -40t + t2 = 0 + 64 Combine like terms: 0 + 64 = 64 -40t + t2 = 64 The t term is -40t. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40t + 400 + t2 = 64 + 400 Reorder the terms: 400 + -40t + t2 = 64 + 400 Combine like terms: 64 + 400 = 464 400 + -40t + t2 = 464 Factor a perfect square on the left side: (t + -20)(t + -20) = 464 Calculate the square root of the right side: 21.540659229 Break this problem into two subproblems by setting (t + -20) equal to 21.540659229 and -21.540659229.Subproblem 1
t + -20 = 21.540659229 Simplifying t + -20 = 21.540659229 Reorder the terms: -20 + t = 21.540659229 Solving -20 + t = 21.540659229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = 21.540659229 + 20 Combine like terms: -20 + 20 = 0 0 + t = 21.540659229 + 20 t = 21.540659229 + 20 Combine like terms: 21.540659229 + 20 = 41.540659229 t = 41.540659229 Simplifying t = 41.540659229Subproblem 2
t + -20 = -21.540659229 Simplifying t + -20 = -21.540659229 Reorder the terms: -20 + t = -21.540659229 Solving -20 + t = -21.540659229 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + t = -21.540659229 + 20 Combine like terms: -20 + 20 = 0 0 + t = -21.540659229 + 20 t = -21.540659229 + 20 Combine like terms: -21.540659229 + 20 = -1.540659229 t = -1.540659229 Simplifying t = -1.540659229Solution
The solution to the problem is based on the solutions from the subproblems. t = {41.540659229, -1.540659229}
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