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Simplifying x + x(2x + -5) = 23 Reorder the terms: x + x(-5 + 2x) = 23 x + (-5 * x + 2x * x) = 23 x + (-5x + 2x2) = 23 Combine like terms: x + -5x = -4x -4x + 2x2 = 23 Solving -4x + 2x2 = 23 Solving for variable 'x'. Reorder the terms: -23 + -4x + 2x2 = 23 + -23 Combine like terms: 23 + -23 = 0 -23 + -4x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -11.5 + -2x + x2 = 0 Move the constant term to the right: Add '11.5' to each side of the equation. -11.5 + -2x + 11.5 + x2 = 0 + 11.5 Reorder the terms: -11.5 + 11.5 + -2x + x2 = 0 + 11.5 Combine like terms: -11.5 + 11.5 = 0.0 0.0 + -2x + x2 = 0 + 11.5 -2x + x2 = 0 + 11.5 Combine like terms: 0 + 11.5 = 11.5 -2x + x2 = 11.5 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 = 11.5 + 1 Reorder the terms: 1 + -2x + x2 = 11.5 + 1 Combine like terms: 11.5 + 1 = 12.5 1 + -2x + x2 = 12.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 12.5 Calculate the square root of the right side: 3.535533906 Break this problem into two subproblems by setting (x + -1) equal to 3.535533906 and -3.535533906.Subproblem 1
x + -1 = 3.535533906 Simplifying x + -1 = 3.535533906 Reorder the terms: -1 + x = 3.535533906 Solving -1 + x = 3.535533906 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 = 3.535533906 + 1 Combine like terms: -1 + 1 = 0 0 + x = 3.535533906 + 1 x = 3.535533906 + 1 Combine like terms: 3.535533906 + 1 = 4.535533906 x = 4.535533906 Simplifying x = 4.535533906Subproblem 2
x + -1 = -3.535533906 Simplifying x + -1 = -3.535533906 Reorder the terms: -1 + x = -3.535533906 Solving -1 + x = -3.535533906 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 = -3.535533906 + 1 Combine like terms: -1 + 1 = 0 0 + x = -3.535533906 + 1 x = -3.535533906 + 1 Combine like terms: -3.535533906 + 1 = -2.535533906 x = -2.535533906 Simplifying x = -2.535533906Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.535533906, -2.535533906}
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