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Simplifying -104 + 6x + x2 = 0 Solving -104 + 6x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '104' to each side of the equation. -104 + 6x + 104 + x2 = 0 + 104 Reorder the terms: -104 + 104 + 6x + x2 = 0 + 104 Combine like terms: -104 + 104 = 0 0 + 6x + x2 = 0 + 104 6x + x2 = 0 + 104 Combine like terms: 0 + 104 = 104 6x + x2 = 104 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 = 104 + 9 Reorder the terms: 9 + 6x + x2 = 104 + 9 Combine like terms: 104 + 9 = 113 9 + 6x + x2 = 113 Factor a perfect square on the left side: (x + 3)(x + 3) = 113 Calculate the square root of the right side: 10.630145813 Break this problem into two subproblems by setting (x + 3) equal to 10.630145813 and -10.630145813.Subproblem 1
x + 3 = 10.630145813 Simplifying x + 3 = 10.630145813 Reorder the terms: 3 + x = 10.630145813 Solving 3 + x = 10.630145813 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 = 10.630145813 + -3 Combine like terms: 3 + -3 = 0 0 + x = 10.630145813 + -3 x = 10.630145813 + -3 Combine like terms: 10.630145813 + -3 = 7.630145813 x = 7.630145813 Simplifying x = 7.630145813Subproblem 2
x + 3 = -10.630145813 Simplifying x + 3 = -10.630145813 Reorder the terms: 3 + x = -10.630145813 Solving 3 + x = -10.630145813 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 = -10.630145813 + -3 Combine like terms: 3 + -3 = 0 0 + x = -10.630145813 + -3 x = -10.630145813 + -3 Combine like terms: -10.630145813 + -3 = -13.630145813 x = -13.630145813 Simplifying x = -13.630145813Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.630145813, -13.630145813}
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