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Simplifying x2 + x + -720 = 0 Reorder the terms: -720 + x + x2 = 0 Solving -720 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '720' to each side of the equation. -720 + x + 720 + x2 = 0 + 720 Reorder the terms: -720 + 720 + x + x2 = 0 + 720 Combine like terms: -720 + 720 = 0 0 + x + x2 = 0 + 720 x + x2 = 0 + 720 Combine like terms: 0 + 720 = 720 x + x2 = 720 The x term is x. 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. x + 0.25 + x2 = 720 + 0.25 Reorder the terms: 0.25 + x + x2 = 720 + 0.25 Combine like terms: 720 + 0.25 = 720.25 0.25 + x + 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 = 26.337473801 x = 26.337473801 Simplifying x = 26.337473801Subproblem 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 = -27.337473801 x = -27.337473801 Simplifying x = -27.337473801Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.337473801, -27.337473801}
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