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Simplifying x2 + -4x + -52 = 0 Reorder the terms: -52 + -4x + x2 = 0 Solving -52 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + -4x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + -4x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + -4x + x2 = 0 + 52 -4x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 -4x + x2 = 52 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 = 52 + 4 Reorder the terms: 4 + -4x + x2 = 52 + 4 Combine like terms: 52 + 4 = 56 4 + -4x + x2 = 56 Factor a perfect square on the left side: (x + -2)(x + -2) = 56 Calculate the square root of the right side: 7.483314774 Break this problem into two subproblems by setting (x + -2) equal to 7.483314774 and -7.483314774.Subproblem 1
x + -2 = 7.483314774 Simplifying x + -2 = 7.483314774 Reorder the terms: -2 + x = 7.483314774 Solving -2 + x = 7.483314774 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 = 7.483314774 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.483314774 + 2 x = 7.483314774 + 2 Combine like terms: 7.483314774 + 2 = 9.483314774 x = 9.483314774 Simplifying x = 9.483314774Subproblem 2
x + -2 = -7.483314774 Simplifying x + -2 = -7.483314774 Reorder the terms: -2 + x = -7.483314774 Solving -2 + x = -7.483314774 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 = -7.483314774 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.483314774 + 2 x = -7.483314774 + 2 Combine like terms: -7.483314774 + 2 = -5.483314774 x = -5.483314774 Simplifying x = -5.483314774Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.483314774, -5.483314774}
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