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Simplifying X2 + -23 = 2X Reorder the terms: -23 + X2 = 2X Solving -23 + X2 = 2X Solving for variable 'X'. Reorder the terms: -23 + -2X + X2 = 2X + -2X Combine like terms: 2X + -2X = 0 -23 + -2X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '23' to each side of the equation. -23 + -2X + 23 + X2 = 0 + 23 Reorder the terms: -23 + 23 + -2X + X2 = 0 + 23 Combine like terms: -23 + 23 = 0 0 + -2X + X2 = 0 + 23 -2X + X2 = 0 + 23 Combine like terms: 0 + 23 = 23 -2X + X2 = 23 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 Reorder the terms: 1 + -2X + X2 = 23 + 1 Combine like terms: 23 + 1 = 24 1 + -2X + X2 = 24 Factor a perfect square on the left side: (X + -1)(X + -1) = 24 Calculate the square root of the right side: 4.898979486 Break this problem into two subproblems by setting (X + -1) equal to 4.898979486 and -4.898979486.Subproblem 1
X + -1 = 4.898979486 Simplifying X + -1 = 4.898979486 Reorder the terms: -1 + X = 4.898979486 Solving -1 + X = 4.898979486 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 = 4.898979486 + 1 Combine like terms: -1 + 1 = 0 0 + X = 4.898979486 + 1 X = 4.898979486 + 1 Combine like terms: 4.898979486 + 1 = 5.898979486 X = 5.898979486 Simplifying X = 5.898979486Subproblem 2
X + -1 = -4.898979486 Simplifying X + -1 = -4.898979486 Reorder the terms: -1 + X = -4.898979486 Solving -1 + X = -4.898979486 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 = -4.898979486 + 1 Combine like terms: -1 + 1 = 0 0 + X = -4.898979486 + 1 X = -4.898979486 + 1 Combine like terms: -4.898979486 + 1 = -3.898979486 X = -3.898979486 Simplifying X = -3.898979486Solution
The solution to the problem is based on the solutions from the subproblems. X = {5.898979486, -3.898979486}
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