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Simplifying x2 + -12x + -38 = 0 Reorder the terms: -38 + -12x + x2 = 0 Solving -38 + -12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '38' to each side of the equation. -38 + -12x + 38 + x2 = 0 + 38 Reorder the terms: -38 + 38 + -12x + x2 = 0 + 38 Combine like terms: -38 + 38 = 0 0 + -12x + x2 = 0 + 38 -12x + x2 = 0 + 38 Combine like terms: 0 + 38 = 38 -12x + x2 = 38 The x term is -12x. Take half its coefficient (-6). Square it (36) and add it to both sides. Add '36' to each side of the equation. -12x + 36 + x2 = 38 + 36 Reorder the terms: 36 + -12x + x2 = 38 + 36 Combine like terms: 38 + 36 = 74 36 + -12x + x2 = 74 Factor a perfect square on the left side: (x + -6)(x + -6) = 74 Calculate the square root of the right side: 8.602325267 Break this problem into two subproblems by setting (x + -6) equal to 8.602325267 and -8.602325267.Subproblem 1
x + -6 = 8.602325267 Simplifying x + -6 = 8.602325267 Reorder the terms: -6 + x = 8.602325267 Solving -6 + x = 8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = 8.602325267 + 6 Combine like terms: -6 + 6 = 0 0 + x = 8.602325267 + 6 x = 8.602325267 + 6 Combine like terms: 8.602325267 + 6 = 14.602325267 x = 14.602325267 Simplifying x = 14.602325267Subproblem 2
x + -6 = -8.602325267 Simplifying x + -6 = -8.602325267 Reorder the terms: -6 + x = -8.602325267 Solving -6 + x = -8.602325267 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '6' to each side of the equation. -6 + 6 + x = -8.602325267 + 6 Combine like terms: -6 + 6 = 0 0 + x = -8.602325267 + 6 x = -8.602325267 + 6 Combine like terms: -8.602325267 + 6 = -2.602325267 x = -2.602325267 Simplifying x = -2.602325267Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.602325267, -2.602325267}
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