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Simplifying x2 + -6x + -32 = 0 Reorder the terms: -32 + -6x + x2 = 0 Solving -32 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '32' to each side of the equation. -32 + -6x + 32 + x2 = 0 + 32 Reorder the terms: -32 + 32 + -6x + x2 = 0 + 32 Combine like terms: -32 + 32 = 0 0 + -6x + x2 = 0 + 32 -6x + x2 = 0 + 32 Combine like terms: 0 + 32 = 32 -6x + x2 = 32 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 = 32 + 9 Reorder the terms: 9 + -6x + x2 = 32 + 9 Combine like terms: 32 + 9 = 41 9 + -6x + x2 = 41 Factor a perfect square on the left side: (x + -3)(x + -3) = 41 Calculate the square root of the right side: 6.403124237 Break this problem into two subproblems by setting (x + -3) equal to 6.403124237 and -6.403124237.Subproblem 1
x + -3 = 6.403124237 Simplifying x + -3 = 6.403124237 Reorder the terms: -3 + x = 6.403124237 Solving -3 + x = 6.403124237 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 = 6.403124237 + 3 Combine like terms: -3 + 3 = 0 0 + x = 6.403124237 + 3 x = 6.403124237 + 3 Combine like terms: 6.403124237 + 3 = 9.403124237 x = 9.403124237 Simplifying x = 9.403124237Subproblem 2
x + -3 = -6.403124237 Simplifying x + -3 = -6.403124237 Reorder the terms: -3 + x = -6.403124237 Solving -3 + x = -6.403124237 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 = -6.403124237 + 3 Combine like terms: -3 + 3 = 0 0 + x = -6.403124237 + 3 x = -6.403124237 + 3 Combine like terms: -6.403124237 + 3 = -3.403124237 x = -3.403124237 Simplifying x = -3.403124237Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.403124237, -3.403124237}
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