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Simplifying 2x + 124 = x2 + -3x Reorder the terms: 124 + 2x = x2 + -3x Reorder the terms: 124 + 2x = -3x + x2 Solving 124 + 2x = -3x + x2 Solving for variable 'x'. Combine like terms: 2x + 3x = 5x 124 + 5x + -1x2 = -3x + x2 + 3x + -1x2 Reorder the terms: 124 + 5x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 124 + 5x + -1x2 = 0 + x2 + -1x2 124 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 124 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -124 + -5x + x2 = 0 Move the constant term to the right: Add '124' to each side of the equation. -124 + -5x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + -5x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + -5x + x2 = 0 + 124 -5x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 -5x + x2 = 124 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 124 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 124 + 6.25 Combine like terms: 124 + 6.25 = 130.25 6.25 + -5x + x2 = 130.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + -2.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + -2.5 = 11.412712211 Simplifying x + -2.5 = 11.412712211 Reorder the terms: -2.5 + x = 11.412712211 Solving -2.5 + x = 11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 11.412712211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 11.412712211 + 2.5 x = 11.412712211 + 2.5 Combine like terms: 11.412712211 + 2.5 = 13.912712211 x = 13.912712211 Simplifying x = 13.912712211Subproblem 2
x + -2.5 = -11.412712211 Simplifying x + -2.5 = -11.412712211 Reorder the terms: -2.5 + x = -11.412712211 Solving -2.5 + x = -11.412712211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -11.412712211 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -11.412712211 + 2.5 x = -11.412712211 + 2.5 Combine like terms: -11.412712211 + 2.5 = -8.912712211 x = -8.912712211 Simplifying x = -8.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.912712211, -8.912712211}
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