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Simplifying x2 + x + -324 = 0 Reorder the terms: -324 + x + x2 = 0 Solving -324 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '324' to each side of the equation. -324 + x + 324 + x2 = 0 + 324 Reorder the terms: -324 + 324 + x + x2 = 0 + 324 Combine like terms: -324 + 324 = 0 0 + x + x2 = 0 + 324 x + x2 = 0 + 324 Combine like terms: 0 + 324 = 324 x + x2 = 324 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 = 324 + 0.25 Reorder the terms: 0.25 + x + x2 = 324 + 0.25 Combine like terms: 324 + 0.25 = 324.25 0.25 + x + x2 = 324.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 324.25 Calculate the square root of the right side: 18.006943105 Break this problem into two subproblems by setting (x + 0.5) equal to 18.006943105 and -18.006943105.Subproblem 1
x + 0.5 = 18.006943105 Simplifying x + 0.5 = 18.006943105 Reorder the terms: 0.5 + x = 18.006943105 Solving 0.5 + x = 18.006943105 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 = 18.006943105 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 18.006943105 + -0.5 x = 18.006943105 + -0.5 Combine like terms: 18.006943105 + -0.5 = 17.506943105 x = 17.506943105 Simplifying x = 17.506943105Subproblem 2
x + 0.5 = -18.006943105 Simplifying x + 0.5 = -18.006943105 Reorder the terms: 0.5 + x = -18.006943105 Solving 0.5 + x = -18.006943105 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 = -18.006943105 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -18.006943105 + -0.5 x = -18.006943105 + -0.5 Combine like terms: -18.006943105 + -0.5 = -18.506943105 x = -18.506943105 Simplifying x = -18.506943105Solution
The solution to the problem is based on the solutions from the subproblems. x = {17.506943105, -18.506943105}
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