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Simplifying x(x + -1) = 720 Reorder the terms: x(-1 + x) = 720 (-1 * x + x * x) = 720 (-1x + x2) = 720 Solving -1x + x2 = 720 Solving for variable 'x'. Reorder the terms: -720 + -1x + x2 = 720 + -720 Combine like terms: 720 + -720 = 0 -720 + -1x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '720' to each side of the equation. -720 + -1x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + -1x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + -1x + x2 = 0 + 720 -1x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 -1x + x2 = 720 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 720 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 720 + 0.25 Combine like terms: 720 + 0.25 = 720.25 0.25 + -1x + x2 = 720.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 720.25 Calculate the square root of the right side: 26.837473801 Break this problem into two subproblems by setting (x + -0.5) equal to 26.837473801 and -26.837473801.Subproblem 1
x + -0.5 = 26.837473801 Simplifying x + -0.5 = 26.837473801 Reorder the terms: -0.5 + x = 26.837473801 Solving -0.5 + x = 26.837473801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 26.837473801 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 26.837473801 + 0.5 x = 26.837473801 + 0.5 Combine like terms: 26.837473801 + 0.5 = 27.337473801 x = 27.337473801 Simplifying x = 27.337473801Subproblem 2
x + -0.5 = -26.837473801 Simplifying x + -0.5 = -26.837473801 Reorder the terms: -0.5 + x = -26.837473801 Solving -0.5 + x = -26.837473801 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -26.837473801 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -26.837473801 + 0.5 x = -26.837473801 + 0.5 Combine like terms: -26.837473801 + 0.5 = -26.337473801 x = -26.337473801 Simplifying x = -26.337473801Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.337473801, -26.337473801}
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