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Simplifying x2 + -1x + -321 = 0 Reorder the terms: -321 + -1x + x2 = 0 Solving -321 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '321' to each side of the equation. -321 + -1x + 321 + x2 = 0 + 321 Reorder the terms: -321 + 321 + -1x + x2 = 0 + 321 Combine like terms: -321 + 321 = 0 0 + -1x + x2 = 0 + 321 -1x + x2 = 0 + 321 Combine like terms: 0 + 321 = 321 -1x + x2 = 321 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 = 321 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 321 + 0.25 Combine like terms: 321 + 0.25 = 321.25 0.25 + -1x + x2 = 321.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 321.25 Calculate the square root of the right side: 17.923448329 Break this problem into two subproblems by setting (x + -0.5) equal to 17.923448329 and -17.923448329.Subproblem 1
x + -0.5 = 17.923448329 Simplifying x + -0.5 = 17.923448329 Reorder the terms: -0.5 + x = 17.923448329 Solving -0.5 + x = 17.923448329 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 = 17.923448329 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 17.923448329 + 0.5 x = 17.923448329 + 0.5 Combine like terms: 17.923448329 + 0.5 = 18.423448329 x = 18.423448329 Simplifying x = 18.423448329Subproblem 2
x + -0.5 = -17.923448329 Simplifying x + -0.5 = -17.923448329 Reorder the terms: -0.5 + x = -17.923448329 Solving -0.5 + x = -17.923448329 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 = -17.923448329 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -17.923448329 + 0.5 x = -17.923448329 + 0.5 Combine like terms: -17.923448329 + 0.5 = -17.423448329 x = -17.423448329 Simplifying x = -17.423448329Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.423448329, -17.423448329}
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