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Simplifying x2 + 6x = 231.125 Reorder the terms: 6x + x2 = 231.125 Solving 6x + x2 = 231.125 Solving for variable 'x'. Reorder the terms: -231.125 + 6x + x2 = 231.125 + -231.125 Combine like terms: 231.125 + -231.125 = 0.000 -231.125 + 6x + x2 = 0.000 Begin completing the square. Move the constant term to the right: Add '231.125' to each side of the equation. -231.125 + 6x + 231.125 + x2 = 0.000 + 231.125 Reorder the terms: -231.125 + 231.125 + 6x + x2 = 0.000 + 231.125 Combine like terms: -231.125 + 231.125 = 0.000 0.000 + 6x + x2 = 0.000 + 231.125 6x + x2 = 0.000 + 231.125 Combine like terms: 0.000 + 231.125 = 231.125 6x + x2 = 231.125 The x term is 6x. Take half its coefficient (3). Square it (9) and add it to both sides. Add '9' to each side of the equation. 6x + 9 + x2 = 231.125 + 9 Reorder the terms: 9 + 6x + x2 = 231.125 + 9 Combine like terms: 231.125 + 9 = 240.125 9 + 6x + x2 = 240.125 Factor a perfect square on the left side: (x + 3)(x + 3) = 240.125 Calculate the square root of the right side: 15.495967217 Break this problem into two subproblems by setting (x + 3) equal to 15.495967217 and -15.495967217.Subproblem 1
x + 3 = 15.495967217 Simplifying x + 3 = 15.495967217 Reorder the terms: 3 + x = 15.495967217 Solving 3 + x = 15.495967217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = 15.495967217 + -3 Combine like terms: 3 + -3 = 0 0 + x = 15.495967217 + -3 x = 15.495967217 + -3 Combine like terms: 15.495967217 + -3 = 12.495967217 x = 12.495967217 Simplifying x = 12.495967217Subproblem 2
x + 3 = -15.495967217 Simplifying x + 3 = -15.495967217 Reorder the terms: 3 + x = -15.495967217 Solving 3 + x = -15.495967217 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + x = -15.495967217 + -3 Combine like terms: 3 + -3 = 0 0 + x = -15.495967217 + -3 x = -15.495967217 + -3 Combine like terms: -15.495967217 + -3 = -18.495967217 x = -18.495967217 Simplifying x = -18.495967217Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.495967217, -18.495967217}
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