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Simplifying x2 + -4x + -56 = 0 Reorder the terms: -56 + -4x + x2 = 0 Solving -56 + -4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '56' to each side of the equation. -56 + -4x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + -4x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + -4x + x2 = 0 + 56 -4x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 -4x + x2 = 56 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 = 56 + 4 Reorder the terms: 4 + -4x + x2 = 56 + 4 Combine like terms: 56 + 4 = 60 4 + -4x + x2 = 60 Factor a perfect square on the left side: (x + -2)(x + -2) = 60 Calculate the square root of the right side: 7.745966692 Break this problem into two subproblems by setting (x + -2) equal to 7.745966692 and -7.745966692.Subproblem 1
x + -2 = 7.745966692 Simplifying x + -2 = 7.745966692 Reorder the terms: -2 + x = 7.745966692 Solving -2 + x = 7.745966692 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 = 7.745966692 + 2 Combine like terms: -2 + 2 = 0 0 + x = 7.745966692 + 2 x = 7.745966692 + 2 Combine like terms: 7.745966692 + 2 = 9.745966692 x = 9.745966692 Simplifying x = 9.745966692Subproblem 2
x + -2 = -7.745966692 Simplifying x + -2 = -7.745966692 Reorder the terms: -2 + x = -7.745966692 Solving -2 + x = -7.745966692 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 = -7.745966692 + 2 Combine like terms: -2 + 2 = 0 0 + x = -7.745966692 + 2 x = -7.745966692 + 2 Combine like terms: -7.745966692 + 2 = -5.745966692 x = -5.745966692 Simplifying x = -5.745966692Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.745966692, -5.745966692}
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