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Simplifying x2 + 7x = 118 Reorder the terms: 7x + x2 = 118 Solving 7x + x2 = 118 Solving for variable 'x'. Reorder the terms: -118 + 7x + x2 = 118 + -118 Combine like terms: 118 + -118 = 0 -118 + 7x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '118' to each side of the equation. -118 + 7x + 118 + x2 = 0 + 118 Reorder the terms: -118 + 118 + 7x + x2 = 0 + 118 Combine like terms: -118 + 118 = 0 0 + 7x + x2 = 0 + 118 7x + x2 = 0 + 118 Combine like terms: 0 + 118 = 118 7x + x2 = 118 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 = 118 + 12.25 Reorder the terms: 12.25 + 7x + x2 = 118 + 12.25 Combine like terms: 118 + 12.25 = 130.25 12.25 + 7x + x2 = 130.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = 130.25 Calculate the square root of the right side: 11.412712211 Break this problem into two subproblems by setting (x + 3.5) equal to 11.412712211 and -11.412712211.Subproblem 1
x + 3.5 = 11.412712211 Simplifying x + 3.5 = 11.412712211 Reorder the terms: 3.5 + x = 11.412712211 Solving 3.5 + x = 11.412712211 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 = 11.412712211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = 11.412712211 + -3.5 x = 11.412712211 + -3.5 Combine like terms: 11.412712211 + -3.5 = 7.912712211 x = 7.912712211 Simplifying x = 7.912712211Subproblem 2
x + 3.5 = -11.412712211 Simplifying x + 3.5 = -11.412712211 Reorder the terms: 3.5 + x = -11.412712211 Solving 3.5 + x = -11.412712211 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 = -11.412712211 + -3.5 Combine like terms: 3.5 + -3.5 = 0.0 0.0 + x = -11.412712211 + -3.5 x = -11.412712211 + -3.5 Combine like terms: -11.412712211 + -3.5 = -14.912712211 x = -14.912712211 Simplifying x = -14.912712211Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.912712211, -14.912712211}
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