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Simplifying t(t + -40) = 21 Reorder the terms: t(-40 + t) = 21 (-40 * t + t * t) = 21 (-40t + t2) = 21 Solving -40t + t2 = 21 Solving for variable 't'. Reorder the terms: -21 + -40t + t2 = 21 + -21 Combine like terms: 21 + -21 = 0 -21 + -40t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '21' to each side of the equation. -21 + -40t + 21 + t2 = 0 + 21 Reorder the terms: -21 + 21 + -40t + t2 = 0 + 21 Combine like terms: -21 + 21 = 0 0 + -40t + t2 = 0 + 21 -40t + t2 = 0 + 21 Combine like terms: 0 + 21 = 21 -40t + t2 = 21 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 = 21 + 400 Reorder the terms: 400 + -40t + t2 = 21 + 400 Combine like terms: 21 + 400 = 421 400 + -40t + t2 = 421 Factor a perfect square on the left side: (t + -20)(t + -20) = 421 Calculate the square root of the right side: 20.518284529 Break this problem into two subproblems by setting (t + -20) equal to 20.518284529 and -20.518284529.Subproblem 1
t + -20 = 20.518284529 Simplifying t + -20 = 20.518284529 Reorder the terms: -20 + t = 20.518284529 Solving -20 + t = 20.518284529 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 = 20.518284529 + 20 Combine like terms: -20 + 20 = 0 0 + t = 20.518284529 + 20 t = 20.518284529 + 20 Combine like terms: 20.518284529 + 20 = 40.518284529 t = 40.518284529 Simplifying t = 40.518284529Subproblem 2
t + -20 = -20.518284529 Simplifying t + -20 = -20.518284529 Reorder the terms: -20 + t = -20.518284529 Solving -20 + t = -20.518284529 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 = -20.518284529 + 20 Combine like terms: -20 + 20 = 0 0 + t = -20.518284529 + 20 t = -20.518284529 + 20 Combine like terms: -20.518284529 + 20 = -0.518284529 t = -0.518284529 Simplifying t = -0.518284529Solution
The solution to the problem is based on the solutions from the subproblems. t = {40.518284529, -0.518284529}
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