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Simplifying x2 + -6x + -230 = 0 Reorder the terms: -230 + -6x + x2 = 0 Solving -230 + -6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '230' to each side of the equation. -230 + -6x + 230 + x2 = 0 + 230 Reorder the terms: -230 + 230 + -6x + x2 = 0 + 230 Combine like terms: -230 + 230 = 0 0 + -6x + x2 = 0 + 230 -6x + x2 = 0 + 230 Combine like terms: 0 + 230 = 230 -6x + x2 = 230 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 = 230 + 9 Reorder the terms: 9 + -6x + x2 = 230 + 9 Combine like terms: 230 + 9 = 239 9 + -6x + x2 = 239 Factor a perfect square on the left side: (x + -3)(x + -3) = 239 Calculate the square root of the right side: 15.459624834 Break this problem into two subproblems by setting (x + -3) equal to 15.459624834 and -15.459624834.Subproblem 1
x + -3 = 15.459624834 Simplifying x + -3 = 15.459624834 Reorder the terms: -3 + x = 15.459624834 Solving -3 + x = 15.459624834 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 = 15.459624834 + 3 Combine like terms: -3 + 3 = 0 0 + x = 15.459624834 + 3 x = 15.459624834 + 3 Combine like terms: 15.459624834 + 3 = 18.459624834 x = 18.459624834 Simplifying x = 18.459624834Subproblem 2
x + -3 = -15.459624834 Simplifying x + -3 = -15.459624834 Reorder the terms: -3 + x = -15.459624834 Solving -3 + x = -15.459624834 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 = -15.459624834 + 3 Combine like terms: -3 + 3 = 0 0 + x = -15.459624834 + 3 x = -15.459624834 + 3 Combine like terms: -15.459624834 + 3 = -12.459624834 x = -12.459624834 Simplifying x = -12.459624834Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.459624834, -12.459624834}
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