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Simplifying t2 + -42t + -80 = 0 Reorder the terms: -80 + -42t + t2 = 0 Solving -80 + -42t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '80' to each side of the equation. -80 + -42t + 80 + t2 = 0 + 80 Reorder the terms: -80 + 80 + -42t + t2 = 0 + 80 Combine like terms: -80 + 80 = 0 0 + -42t + t2 = 0 + 80 -42t + t2 = 0 + 80 Combine like terms: 0 + 80 = 80 -42t + t2 = 80 The t term is -42t. Take half its coefficient (-21). Square it (441) and add it to both sides. Add '441' to each side of the equation. -42t + 441 + t2 = 80 + 441 Reorder the terms: 441 + -42t + t2 = 80 + 441 Combine like terms: 80 + 441 = 521 441 + -42t + t2 = 521 Factor a perfect square on the left side: (t + -21)(t + -21) = 521 Calculate the square root of the right side: 22.825424421 Break this problem into two subproblems by setting (t + -21) equal to 22.825424421 and -22.825424421.Subproblem 1
t + -21 = 22.825424421 Simplifying t + -21 = 22.825424421 Reorder the terms: -21 + t = 22.825424421 Solving -21 + t = 22.825424421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + t = 22.825424421 + 21 Combine like terms: -21 + 21 = 0 0 + t = 22.825424421 + 21 t = 22.825424421 + 21 Combine like terms: 22.825424421 + 21 = 43.825424421 t = 43.825424421 Simplifying t = 43.825424421Subproblem 2
t + -21 = -22.825424421 Simplifying t + -21 = -22.825424421 Reorder the terms: -21 + t = -22.825424421 Solving -21 + t = -22.825424421 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '21' to each side of the equation. -21 + 21 + t = -22.825424421 + 21 Combine like terms: -21 + 21 = 0 0 + t = -22.825424421 + 21 t = -22.825424421 + 21 Combine like terms: -22.825424421 + 21 = -1.825424421 t = -1.825424421 Simplifying t = -1.825424421Solution
The solution to the problem is based on the solutions from the subproblems. t = {43.825424421, -1.825424421}
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