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Simplifying x2 + -1 = 73x Reorder the terms: -1 + x2 = 73x Solving -1 + x2 = 73x Solving for variable 'x'. Reorder the terms: -1 + -73x + x2 = 73x + -73x Combine like terms: 73x + -73x = 0 -1 + -73x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '1' to each side of the equation. -1 + -73x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + -73x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -73x + x2 = 0 + 1 -73x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 -73x + x2 = 1 The x term is -73x. Take half its coefficient (-36.5). Square it (1332.25) and add it to both sides. Add '1332.25' to each side of the equation. -73x + 1332.25 + x2 = 1 + 1332.25 Reorder the terms: 1332.25 + -73x + x2 = 1 + 1332.25 Combine like terms: 1 + 1332.25 = 1333.25 1332.25 + -73x + x2 = 1333.25 Factor a perfect square on the left side: (x + -36.5)(x + -36.5) = 1333.25 Calculate the square root of the right side: 36.513696061 Break this problem into two subproblems by setting (x + -36.5) equal to 36.513696061 and -36.513696061.Subproblem 1
x + -36.5 = 36.513696061 Simplifying x + -36.5 = 36.513696061 Reorder the terms: -36.5 + x = 36.513696061 Solving -36.5 + x = 36.513696061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.5' to each side of the equation. -36.5 + 36.5 + x = 36.513696061 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = 36.513696061 + 36.5 x = 36.513696061 + 36.5 Combine like terms: 36.513696061 + 36.5 = 73.013696061 x = 73.013696061 Simplifying x = 73.013696061Subproblem 2
x + -36.5 = -36.513696061 Simplifying x + -36.5 = -36.513696061 Reorder the terms: -36.5 + x = -36.513696061 Solving -36.5 + x = -36.513696061 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '36.5' to each side of the equation. -36.5 + 36.5 + x = -36.513696061 + 36.5 Combine like terms: -36.5 + 36.5 = 0.0 0.0 + x = -36.513696061 + 36.5 x = -36.513696061 + 36.5 Combine like terms: -36.513696061 + 36.5 = -0.013696061 x = -0.013696061 Simplifying x = -0.013696061Solution
The solution to the problem is based on the solutions from the subproblems. x = {73.013696061, -0.013696061}
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