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Simplifying x2 = 39x + -40 Reorder the terms: x2 = -40 + 39x Solving x2 = -40 + 39x Solving for variable 'x'. Reorder the terms: 40 + -39x + x2 = -40 + 39x + 40 + -39x Reorder the terms: 40 + -39x + x2 = -40 + 40 + 39x + -39x Combine like terms: -40 + 40 = 0 40 + -39x + x2 = 0 + 39x + -39x 40 + -39x + x2 = 39x + -39x Combine like terms: 39x + -39x = 0 40 + -39x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + -39x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + -39x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + -39x + x2 = 0 + -40 -39x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 -39x + x2 = -40 The x term is -39x. Take half its coefficient (-19.5). Square it (380.25) and add it to both sides. Add '380.25' to each side of the equation. -39x + 380.25 + x2 = -40 + 380.25 Reorder the terms: 380.25 + -39x + x2 = -40 + 380.25 Combine like terms: -40 + 380.25 = 340.25 380.25 + -39x + x2 = 340.25 Factor a perfect square on the left side: (x + -19.5)(x + -19.5) = 340.25 Calculate the square root of the right side: 18.445866746 Break this problem into two subproblems by setting (x + -19.5) equal to 18.445866746 and -18.445866746.Subproblem 1
x + -19.5 = 18.445866746 Simplifying x + -19.5 = 18.445866746 Reorder the terms: -19.5 + x = 18.445866746 Solving -19.5 + x = 18.445866746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = 18.445866746 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = 18.445866746 + 19.5 x = 18.445866746 + 19.5 Combine like terms: 18.445866746 + 19.5 = 37.945866746 x = 37.945866746 Simplifying x = 37.945866746Subproblem 2
x + -19.5 = -18.445866746 Simplifying x + -19.5 = -18.445866746 Reorder the terms: -19.5 + x = -18.445866746 Solving -19.5 + x = -18.445866746 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '19.5' to each side of the equation. -19.5 + 19.5 + x = -18.445866746 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + x = -18.445866746 + 19.5 x = -18.445866746 + 19.5 Combine like terms: -18.445866746 + 19.5 = 1.054133254 x = 1.054133254 Simplifying x = 1.054133254Solution
The solution to the problem is based on the solutions from the subproblems. x = {37.945866746, 1.054133254}
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