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Simplifying x2 + -2x + -143.23 = -12.554 Reorder the terms: -143.23 + -2x + x2 = -12.554 Solving -143.23 + -2x + x2 = -12.554 Solving for variable 'x'. Reorder the terms: -143.23 + 12.554 + -2x + x2 = -12.554 + 12.554 Combine like terms: -143.23 + 12.554 = -130.676 -130.676 + -2x + x2 = -12.554 + 12.554 Combine like terms: -12.554 + 12.554 = 0.000 -130.676 + -2x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '130.676' to each side of the equation. -130.676 + -2x + 130.676 + x2 = 0.000 + 130.676 Reorder the terms: -130.676 + 130.676 + -2x + x2 = 0.000 + 130.676 Combine like terms: -130.676 + 130.676 = 0.000 0.000 + -2x + x2 = 0.000 + 130.676 -2x + x2 = 0.000 + 130.676 Combine like terms: 0.000 + 130.676 = 130.676 -2x + x2 = 130.676 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 = 130.676 + 1 Reorder the terms: 1 + -2x + x2 = 130.676 + 1 Combine like terms: 130.676 + 1 = 131.676 1 + -2x + x2 = 131.676 Factor a perfect square on the left side: (x + -1)(x + -1) = 131.676 Calculate the square root of the right side: 11.47501634 Break this problem into two subproblems by setting (x + -1) equal to 11.47501634 and -11.47501634.Subproblem 1
x + -1 = 11.47501634 Simplifying x + -1 = 11.47501634 Reorder the terms: -1 + x = 11.47501634 Solving -1 + x = 11.47501634 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 = 11.47501634 + 1 Combine like terms: -1 + 1 = 0 0 + x = 11.47501634 + 1 x = 11.47501634 + 1 Combine like terms: 11.47501634 + 1 = 12.47501634 x = 12.47501634 Simplifying x = 12.47501634Subproblem 2
x + -1 = -11.47501634 Simplifying x + -1 = -11.47501634 Reorder the terms: -1 + x = -11.47501634 Solving -1 + x = -11.47501634 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 = -11.47501634 + 1 Combine like terms: -1 + 1 = 0 0 + x = -11.47501634 + 1 x = -11.47501634 + 1 Combine like terms: -11.47501634 + 1 = -10.47501634 x = -10.47501634 Simplifying x = -10.47501634Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.47501634, -10.47501634}
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