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Simplifying x2 + 7x = 124 Reorder the terms: 7x + x2 = 124 Solving 7x + x2 = 124 Solving for variable 'x'. Reorder the terms: -124 + 7x + x2 = 124 + -124 Combine like terms: 124 + -124 = 0 -124 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '124' to each side of the equation. -124 + 7x + 124 + x2 = 0 + 124 Reorder the terms: -124 + 124 + 7x + x2 = 0 + 124 Combine like terms: -124 + 124 = 0 0 + 7x + x2 = 0 + 124 7x + x2 = 0 + 124 Combine like terms: 0 + 124 = 124 7x + x2 = 124 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = 124 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 124 + 12.25 Combine like terms: 124 + 12.25 = 136.25 12.25 + 7x + x2 = 136.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 136.25 Calculate the square root of the right side: 11.67261753 Break this problem into two subproblems by setting (x + 3.5) equal to 11.67261753 and -11.67261753.Subproblem 1
x + 3.5 = 11.67261753 Simplifying x + 3.5 = 11.67261753 Reorder the terms: 3.5 + x = 11.67261753 Solving 3.5 + x = 11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = 11.67261753 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.67261753 + -3.5 x = 11.67261753 + -3.5 Combine like terms: 11.67261753 + -3.5 = 8.17261753 x = 8.17261753 Simplifying x = 8.17261753Subproblem 2
x + 3.5 = -11.67261753 Simplifying x + 3.5 = -11.67261753 Reorder the terms: 3.5 + x = -11.67261753 Solving 3.5 + x = -11.67261753 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3.5' to each side of the equation. 3.5 + -3.5 + x = -11.67261753 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.67261753 + -3.5 x = -11.67261753 + -3.5 Combine like terms: -11.67261753 + -3.5 = -15.17261753 x = -15.17261753 Simplifying x = -15.17261753Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.17261753, -15.17261753}
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