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Simplifying x2 + -1x + -432 = 0 Reorder the terms: -432 + -1x + x2 = 0 Solving -432 + -1x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '432' to each side of the equation. -432 + -1x + 432 + x2 = 0 + 432 Reorder the terms: -432 + 432 + -1x + x2 = 0 + 432 Combine like terms: -432 + 432 = 0 0 + -1x + x2 = 0 + 432 -1x + x2 = 0 + 432 Combine like terms: 0 + 432 = 432 -1x + x2 = 432 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 = 432 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 432 + 0.25 Combine like terms: 432 + 0.25 = 432.25 0.25 + -1x + x2 = 432.25 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 432.25 Calculate the square root of the right side: 20.790622886 Break this problem into two subproblems by setting (x + -0.5) equal to 20.790622886 and -20.790622886.Subproblem 1
x + -0.5 = 20.790622886 Simplifying x + -0.5 = 20.790622886 Reorder the terms: -0.5 + x = 20.790622886 Solving -0.5 + x = 20.790622886 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 = 20.790622886 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 20.790622886 + 0.5 x = 20.790622886 + 0.5 Combine like terms: 20.790622886 + 0.5 = 21.290622886 x = 21.290622886 Simplifying x = 21.290622886Subproblem 2
x + -0.5 = -20.790622886 Simplifying x + -0.5 = -20.790622886 Reorder the terms: -0.5 + x = -20.790622886 Solving -0.5 + x = -20.790622886 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 = -20.790622886 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -20.790622886 + 0.5 x = -20.790622886 + 0.5 Combine like terms: -20.790622886 + 0.5 = -20.290622886 x = -20.290622886 Simplifying x = -20.290622886Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.290622886, -20.290622886}
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