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Simplifying x2 + -6x + -934 = 0 Reorder the terms: -934 + -6x + x2 = 0 Solving -934 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '934' to each side of the equation. -934 + -6x + 934 + x2 = 0 + 934 Reorder the terms: -934 + 934 + -6x + x2 = 0 + 934 Combine like terms: -934 + 934 = 0 0 + -6x + x2 = 0 + 934 -6x + x2 = 0 + 934 Combine like terms: 0 + 934 = 934 -6x + x2 = 934 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 = 934 + 9 Reorder the terms: 9 + -6x + x2 = 934 + 9 Combine like terms: 934 + 9 = 943 9 + -6x + x2 = 943 Factor a perfect square on the left side: (x + -3)(x + -3) = 943 Calculate the square root of the right side: 30.708305066 Break this problem into two subproblems by setting (x + -3) equal to 30.708305066 and -30.708305066.Subproblem 1
x + -3 = 30.708305066 Simplifying x + -3 = 30.708305066 Reorder the terms: -3 + x = 30.708305066 Solving -3 + x = 30.708305066 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 = 30.708305066 + 3 Combine like terms: -3 + 3 = 0 0 + x = 30.708305066 + 3 x = 30.708305066 + 3 Combine like terms: 30.708305066 + 3 = 33.708305066 x = 33.708305066 Simplifying x = 33.708305066Subproblem 2
x + -3 = -30.708305066 Simplifying x + -3 = -30.708305066 Reorder the terms: -3 + x = -30.708305066 Solving -3 + x = -30.708305066 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 = -30.708305066 + 3 Combine like terms: -3 + 3 = 0 0 + x = -30.708305066 + 3 x = -30.708305066 + 3 Combine like terms: -30.708305066 + 3 = -27.708305066 x = -27.708305066 Simplifying x = -27.708305066Solution
The solution to the problem is based on the solutions from the subproblems. x = {33.708305066, -27.708305066}
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