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Simplifying x2 + -4x + -729 = 0 Reorder the terms: -729 + -4x + x2 = 0 Solving -729 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '729' to each side of the equation. -729 + -4x + 729 + x2 = 0 + 729 Reorder the terms: -729 + 729 + -4x + x2 = 0 + 729 Combine like terms: -729 + 729 = 0 0 + -4x + x2 = 0 + 729 -4x + x2 = 0 + 729 Combine like terms: 0 + 729 = 729 -4x + x2 = 729 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 729 + 4 Reorder the terms: 4 + -4x + x2 = 729 + 4 Combine like terms: 729 + 4 = 733 4 + -4x + x2 = 733 Factor a perfect square on the left side: (x + -2)(x + -2) = 733 Calculate the square root of the right side: 27.073972741 Break this problem into two subproblems by setting (x + -2) equal to 27.073972741 and -27.073972741.Subproblem 1
x + -2 = 27.073972741 Simplifying x + -2 = 27.073972741 Reorder the terms: -2 + x = 27.073972741 Solving -2 + x = 27.073972741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 27.073972741 + 2 Combine like terms: -2 + 2 = 0 0 + x = 27.073972741 + 2 x = 27.073972741 + 2 Combine like terms: 27.073972741 + 2 = 29.073972741 x = 29.073972741 Simplifying x = 29.073972741Subproblem 2
x + -2 = -27.073972741 Simplifying x + -2 = -27.073972741 Reorder the terms: -2 + x = -27.073972741 Solving -2 + x = -27.073972741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -27.073972741 + 2 Combine like terms: -2 + 2 = 0 0 + x = -27.073972741 + 2 x = -27.073972741 + 2 Combine like terms: -27.073972741 + 2 = -25.073972741 x = -25.073972741 Simplifying x = -25.073972741Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.073972741, -25.073972741}
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