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Simplifying x2 + -2x + -23.1 = 0 Reorder the terms: -23.1 + -2x + x2 = 0 Solving -23.1 + -2x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '23.1' to each side of the equation. -23.1 + -2x + 23.1 + x2 = 0 + 23.1 Reorder the terms: -23.1 + 23.1 + -2x + x2 = 0 + 23.1 Combine like terms: -23.1 + 23.1 = 0.0 0.0 + -2x + x2 = 0 + 23.1 -2x + x2 = 0 + 23.1 Combine like terms: 0 + 23.1 = 23.1 -2x + x2 = 23.1 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 23.1 + 1 Reorder the terms: 1 + -2x + x2 = 23.1 + 1 Combine like terms: 23.1 + 1 = 24.1 1 + -2x + x2 = 24.1 Factor a perfect square on the left side: (x + -1)(x + -1) = 24.1 Calculate the square root of the right side: 4.909175083 Break this problem into two subproblems by setting (x + -1) equal to 4.909175083 and -4.909175083.Subproblem 1
x + -1 = 4.909175083 Simplifying x + -1 = 4.909175083 Reorder the terms: -1 + x = 4.909175083 Solving -1 + x = 4.909175083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 4.909175083 + 1 Combine like terms: -1 + 1 = 0 0 + x = 4.909175083 + 1 x = 4.909175083 + 1 Combine like terms: 4.909175083 + 1 = 5.909175083 x = 5.909175083 Simplifying x = 5.909175083Subproblem 2
x + -1 = -4.909175083 Simplifying x + -1 = -4.909175083 Reorder the terms: -1 + x = -4.909175083 Solving -1 + x = -4.909175083 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -4.909175083 + 1 Combine like terms: -1 + 1 = 0 0 + x = -4.909175083 + 1 x = -4.909175083 + 1 Combine like terms: -4.909175083 + 1 = -3.909175083 x = -3.909175083 Simplifying x = -3.909175083Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.909175083, -3.909175083}
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