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Simplifying t * t + 40t + -400 = 0 Multiply t * t t2 + 40t + -400 = 0 Reorder the terms: -400 + 40t + t2 = 0 Solving -400 + 40t + t2 = 0 Solving for variable 't'. Begin completing the square. Move the constant term to the right: Add '400' to each side of the equation. -400 + 40t + 400 + t2 = 0 + 400 Reorder the terms: -400 + 400 + 40t + t2 = 0 + 400 Combine like terms: -400 + 400 = 0 0 + 40t + t2 = 0 + 400 40t + t2 = 0 + 400 Combine like terms: 0 + 400 = 400 40t + t2 = 400 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 = 400 + 400 Reorder the terms: 400 + 40t + t2 = 400 + 400 Combine like terms: 400 + 400 = 800 400 + 40t + t2 = 800 Factor a perfect square on the left side: (t + 20)(t + 20) = 800 Calculate the square root of the right side: 28.284271247 Break this problem into two subproblems by setting (t + 20) equal to 28.284271247 and -28.284271247.Subproblem 1
t + 20 = 28.284271247 Simplifying t + 20 = 28.284271247 Reorder the terms: 20 + t = 28.284271247 Solving 20 + t = 28.284271247 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 = 28.284271247 + -20 Combine like terms: 20 + -20 = 0 0 + t = 28.284271247 + -20 t = 28.284271247 + -20 Combine like terms: 28.284271247 + -20 = 8.284271247 t = 8.284271247 Simplifying t = 8.284271247Subproblem 2
t + 20 = -28.284271247 Simplifying t + 20 = -28.284271247 Reorder the terms: 20 + t = -28.284271247 Solving 20 + t = -28.284271247 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 = -28.284271247 + -20 Combine like terms: 20 + -20 = 0 0 + t = -28.284271247 + -20 t = -28.284271247 + -20 Combine like terms: -28.284271247 + -20 = -48.284271247 t = -48.284271247 Simplifying t = -48.284271247Solution
The solution to the problem is based on the solutions from the subproblems. t = {8.284271247, -48.284271247}
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