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Simplifying 2x2 + -4x + -123 = 0 Reorder the terms: -123 + -4x + 2x2 = 0 Solving -123 + -4x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -61.5 + -2x + x2 = 0 Move the constant term to the right: Add '61.5' to each side of the equation. -61.5 + -2x + 61.5 + x2 = 0 + 61.5 Reorder the terms: -61.5 + 61.5 + -2x + x2 = 0 + 61.5 Combine like terms: -61.5 + 61.5 = 0.0 0.0 + -2x + x2 = 0 + 61.5 -2x + x2 = 0 + 61.5 Combine like terms: 0 + 61.5 = 61.5 -2x + x2 = 61.5 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 = 61.5 + 1 Reorder the terms: 1 + -2x + x2 = 61.5 + 1 Combine like terms: 61.5 + 1 = 62.5 1 + -2x + x2 = 62.5 Factor a perfect square on the left side: (x + -1)(x + -1) = 62.5 Calculate the square root of the right side: 7.90569415 Break this problem into two subproblems by setting (x + -1) equal to 7.90569415 and -7.90569415.Subproblem 1
x + -1 = 7.90569415 Simplifying x + -1 = 7.90569415 Reorder the terms: -1 + x = 7.90569415 Solving -1 + x = 7.90569415 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 = 7.90569415 + 1 Combine like terms: -1 + 1 = 0 0 + x = 7.90569415 + 1 x = 7.90569415 + 1 Combine like terms: 7.90569415 + 1 = 8.90569415 x = 8.90569415 Simplifying x = 8.90569415Subproblem 2
x + -1 = -7.90569415 Simplifying x + -1 = -7.90569415 Reorder the terms: -1 + x = -7.90569415 Solving -1 + x = -7.90569415 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 = -7.90569415 + 1 Combine like terms: -1 + 1 = 0 0 + x = -7.90569415 + 1 x = -7.90569415 + 1 Combine like terms: -7.90569415 + 1 = -6.90569415 x = -6.90569415 Simplifying x = -6.90569415Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.90569415, -6.90569415}
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