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Simplifying x2 + -1x + -364 = 0 Reorder the terms: -364 + -1x + x2 = 0 Solving -364 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '364' to each side of the equation. -364 + -1x + 364 + x2 = 0 + 364 Reorder the terms: -364 + 364 + -1x + x2 = 0 + 364 Combine like terms: -364 + 364 = 0 0 + -1x + x2 = 0 + 364 -1x + x2 = 0 + 364 Combine like terms: 0 + 364 = 364 -1x + x2 = 364 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 = 364 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 364 + 0.25 Combine like terms: 364 + 0.25 = 364.25 0.25 + -1x + x2 = 364.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 364.25 Calculate the square root of the right side: 19.085334684 Break this problem into two subproblems by setting (x + -0.5) equal to 19.085334684 and -19.085334684.Subproblem 1
x + -0.5 = 19.085334684 Simplifying x + -0.5 = 19.085334684 Reorder the terms: -0.5 + x = 19.085334684 Solving -0.5 + x = 19.085334684 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 = 19.085334684 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 19.085334684 + 0.5 x = 19.085334684 + 0.5 Combine like terms: 19.085334684 + 0.5 = 19.585334684 x = 19.585334684 Simplifying x = 19.585334684Subproblem 2
x + -0.5 = -19.085334684 Simplifying x + -0.5 = -19.085334684 Reorder the terms: -0.5 + x = -19.085334684 Solving -0.5 + x = -19.085334684 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 = -19.085334684 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -19.085334684 + 0.5 x = -19.085334684 + 0.5 Combine like terms: -19.085334684 + 0.5 = -18.585334684 x = -18.585334684 Simplifying x = -18.585334684Solution
The solution to the problem is based on the solutions from the subproblems. x = {19.585334684, -18.585334684}
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