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Simplifying x2 + -40 + -8x = 0 Reorder the terms: -40 + -8x + x2 = 0 Solving -40 + -8x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '40' to each side of the equation. -40 + -8x + 40 + x2 = 0 + 40 Reorder the terms: -40 + 40 + -8x + x2 = 0 + 40 Combine like terms: -40 + 40 = 0 0 + -8x + x2 = 0 + 40 -8x + x2 = 0 + 40 Combine like terms: 0 + 40 = 40 -8x + x2 = 40 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = 40 + 16 Reorder the terms: 16 + -8x + x2 = 40 + 16 Combine like terms: 40 + 16 = 56 16 + -8x + x2 = 56 Factor a perfect square on the left side: (x + -4)(x + -4) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -4) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -4 = 7.483314774 Simplifying x + -4 = 7.483314774 Reorder the terms: -4 + x = 7.483314774 Solving -4 + x = 7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 7.483314774 + 4 Combine like terms: -4 + 4 = 0 0 + x = 7.483314774 + 4 x = 7.483314774 + 4 Combine like terms: 7.483314774 + 4 = 11.483314774 x = 11.483314774 Simplifying x = 11.483314774Subproblem 2
x + -4 = -7.483314774 Simplifying x + -4 = -7.483314774 Reorder the terms: -4 + x = -7.483314774 Solving -4 + x = -7.483314774 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -7.483314774 + 4 Combine like terms: -4 + 4 = 0 0 + x = -7.483314774 + 4 x = -7.483314774 + 4 Combine like terms: -7.483314774 + 4 = -3.483314774 x = -3.483314774 Simplifying x = -3.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.483314774, -3.483314774}
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