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Simplifying 1400 = 80t + -1t2 Solving 1400 = 80t + -1t2 Solving for variable 't'. Reorder the terms: 1400 + -80t + t2 = 80t + -80t + -1t2 + t2 Combine like terms: 80t + -80t = 0 1400 + -80t + t2 = 0 + -1t2 + t2 1400 + -80t + t2 = -1t2 + t2 Combine like terms: -1t2 + t2 = 0 1400 + -80t + t2 = 0 Begin completing the square. Move the constant term to the right: Add '-1400' to each side of the equation. 1400 + -80t + -1400 + t2 = 0 + -1400 Reorder the terms: 1400 + -1400 + -80t + t2 = 0 + -1400 Combine like terms: 1400 + -1400 = 0 0 + -80t + t2 = 0 + -1400 -80t + t2 = 0 + -1400 Combine like terms: 0 + -1400 = -1400 -80t + t2 = -1400 The t term is -80t. Take half its coefficient (-40). Square it (1600) and add it to both sides. Add '1600' to each side of the equation. -80t + 1600 + t2 = -1400 + 1600 Reorder the terms: 1600 + -80t + t2 = -1400 + 1600 Combine like terms: -1400 + 1600 = 200 1600 + -80t + t2 = 200 Factor a perfect square on the left side: (t + -40)(t + -40) = 200 Calculate the square root of the right side: 14.142135624 Break this problem into two subproblems by setting (t + -40) equal to 14.142135624 and -14.142135624.Subproblem 1
t + -40 = 14.142135624 Simplifying t + -40 = 14.142135624 Reorder the terms: -40 + t = 14.142135624 Solving -40 + t = 14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + t = 14.142135624 + 40 Combine like terms: -40 + 40 = 0 0 + t = 14.142135624 + 40 t = 14.142135624 + 40 Combine like terms: 14.142135624 + 40 = 54.142135624 t = 54.142135624 Simplifying t = 54.142135624Subproblem 2
t + -40 = -14.142135624 Simplifying t + -40 = -14.142135624 Reorder the terms: -40 + t = -14.142135624 Solving -40 + t = -14.142135624 Solving for variable 't'. Move all terms containing t to the left, all other terms to the right. Add '40' to each side of the equation. -40 + 40 + t = -14.142135624 + 40 Combine like terms: -40 + 40 = 0 0 + t = -14.142135624 + 40 t = -14.142135624 + 40 Combine like terms: -14.142135624 + 40 = 25.857864376 t = 25.857864376 Simplifying t = 25.857864376Solution
The solution to the problem is based on the solutions from the subproblems. t = {54.142135624, 25.857864376}
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