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Simplifying 3x + x * x = 124 Multiply x * x 3x + x2 = 124 Solving 3x + x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 3x + x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 3x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + 3x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 3x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 3x + x2 = 0 + 124 3x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 3x + x2 = 124 The x term is 3x. Take half its coefficient (1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. 3x + 2.25 + x2 = 124 + 2.25 Reorder the terms: 2.25 + 3x + x2 = 124 + 2.25 Combine like terms: 124 + 2.25 = 126.25 2.25 + 3x + x2 = 126.25 Factor a perfect square on the left side: (x + 1.5)(x + 1.5) = 126.25 Calculate the square root of the right side: 11.236102527 Break this problem into two subproblems by setting (x + 1.5) equal to 11.236102527 and -11.236102527.Subproblem 1
x + 1.5 = 11.236102527 Simplifying x + 1.5 = 11.236102527 Reorder the terms: 1.5 + x = 11.236102527 Solving 1.5 + x = 11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = 11.236102527 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = 11.236102527 + -1.5 x = 11.236102527 + -1.5 Combine like terms: 11.236102527 + -1.5 = 9.736102527 x = 9.736102527 Simplifying x = 9.736102527Subproblem 2
x + 1.5 = -11.236102527 Simplifying x + 1.5 = -11.236102527 Reorder the terms: 1.5 + x = -11.236102527 Solving 1.5 + x = -11.236102527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.5' to each side of the equation. 1.5 + -1.5 + x = -11.236102527 + -1.5 Combine like terms: 1.5 + -1.5 = 0.0 0.0 + x = -11.236102527 + -1.5 x = -11.236102527 + -1.5 Combine like terms: -11.236102527 + -1.5 = -12.736102527 x = -12.736102527 Simplifying x = -12.736102527Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.736102527, -12.736102527}
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