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Simplifying (2x2) + -12x + -39 = 0 Reorder the terms: -39 + -12x + (2x2) = 0 Solving -39 + -12x + (2x2) = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -19.5 + -6x + x2 = 0 Move the constant term to the right: Add '19.5' to each side of the equation. -19.5 + -6x + 19.5 + x2 = 0 + 19.5 Reorder the terms: -19.5 + 19.5 + -6x + x2 = 0 + 19.5 Combine like terms: -19.5 + 19.5 = 0.0 0.0 + -6x + x2 = 0 + 19.5 -6x + x2 = 0 + 19.5 Combine like terms: 0 + 19.5 = 19.5 -6x + x2 = 19.5 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 = 19.5 + 9 Reorder the terms: 9 + -6x + x2 = 19.5 + 9 Combine like terms: 19.5 + 9 = 28.5 9 + -6x + x2 = 28.5 Factor a perfect square on the left side: ((x) + -3)((x) + -3) = 28.5 Calculate the square root of the right side: 5.338539126 Break this problem into two subproblems by setting ((x) + -3) equal to 5.338539126 and -5.338539126.Subproblem 1
(x) + -3 = 5.338539126 Simplifying (x) + -3 = 5.338539126 x + -3 = 5.338539126 Reorder the terms: -3 + x = 5.338539126 Solving -3 + x = 5.338539126 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 = 5.338539126 + 3 Combine like terms: -3 + 3 = 0 0 + x = 5.338539126 + 3 x = 5.338539126 + 3 Combine like terms: 5.338539126 + 3 = 8.338539126 x = 8.338539126 Simplifying x = 8.338539126Subproblem 2
(x) + -3 = -5.338539126 Simplifying (x) + -3 = -5.338539126 x + -3 = -5.338539126 Reorder the terms: -3 + x = -5.338539126 Solving -3 + x = -5.338539126 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 = -5.338539126 + 3 Combine like terms: -3 + 3 = 0 0 + x = -5.338539126 + 3 x = -5.338539126 + 3 Combine like terms: -5.338539126 + 3 = -2.338539126 x = -2.338539126 Simplifying x = -2.338539126Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.338539126, -2.338539126}
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