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Simplifying x(x) + 6x + -864 = 0 Multiply x * x x2 + 6x + -864 = 0 Reorder the terms: -864 + 6x + x2 = 0 Solving -864 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '864' to each side of the equation. -864 + 6x + 864 + x2 = 0 + 864 Reorder the terms: -864 + 864 + 6x + x2 = 0 + 864 Combine like terms: -864 + 864 = 0 0 + 6x + x2 = 0 + 864 6x + x2 = 0 + 864 Combine like terms: 0 + 864 = 864 6x + x2 = 864 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 864 + 9 Reorder the terms: 9 + 6x + x2 = 864 + 9 Combine like terms: 864 + 9 = 873 9 + 6x + x2 = 873 Factor a perfect square on the left side: (x + 3)(x + 3) = 873 Calculate the square root of the right side: 29.546573405 Break this problem into two subproblems by setting (x + 3) equal to 29.546573405 and -29.546573405.Subproblem 1
x + 3 = 29.546573405 Simplifying x + 3 = 29.546573405 Reorder the terms: 3 + x = 29.546573405 Solving 3 + x = 29.546573405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 29.546573405 + -3 Combine like terms: 3 + -3 = 0 0 + x = 29.546573405 + -3 x = 29.546573405 + -3 Combine like terms: 29.546573405 + -3 = 26.546573405 x = 26.546573405 Simplifying x = 26.546573405Subproblem 2
x + 3 = -29.546573405 Simplifying x + 3 = -29.546573405 Reorder the terms: 3 + x = -29.546573405 Solving 3 + x = -29.546573405 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -29.546573405 + -3 Combine like terms: 3 + -3 = 0 0 + x = -29.546573405 + -3 x = -29.546573405 + -3 Combine like terms: -29.546573405 + -3 = -32.546573405 x = -32.546573405 Simplifying x = -32.546573405Solution
The solution to the problem is based on the solutions from the subproblems. x = {26.546573405, -32.546573405}
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