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Simplifying x2 + 12x + -6 = 46 Reorder the terms: -6 + 12x + x2 = 46 Solving -6 + 12x + x2 = 46 Solving for variable 'x'. Reorder the terms: -6 + -46 + 12x + x2 = 46 + -46 Combine like terms: -6 + -46 = -52 -52 + 12x + x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -52 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '52' to each side of the equation. -52 + 12x + 52 + x2 = 0 + 52 Reorder the terms: -52 + 52 + 12x + x2 = 0 + 52 Combine like terms: -52 + 52 = 0 0 + 12x + x2 = 0 + 52 12x + x2 = 0 + 52 Combine like terms: 0 + 52 = 52 12x + x2 = 52 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 = 52 + 36 Reorder the terms: 36 + 12x + x2 = 52 + 36 Combine like terms: 52 + 36 = 88 36 + 12x + x2 = 88 Factor a perfect square on the left side: (x + 6)(x + 6) = 88 Calculate the square root of the right side: 9.38083152 Break this problem into two subproblems by setting (x + 6) equal to 9.38083152 and -9.38083152.Subproblem 1
x + 6 = 9.38083152 Simplifying x + 6 = 9.38083152 Reorder the terms: 6 + x = 9.38083152 Solving 6 + x = 9.38083152 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 = 9.38083152 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.38083152 + -6 x = 9.38083152 + -6 Combine like terms: 9.38083152 + -6 = 3.38083152 x = 3.38083152 Simplifying x = 3.38083152Subproblem 2
x + 6 = -9.38083152 Simplifying x + 6 = -9.38083152 Reorder the terms: 6 + x = -9.38083152 Solving 6 + x = -9.38083152 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 = -9.38083152 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.38083152 + -6 x = -9.38083152 + -6 Combine like terms: -9.38083152 + -6 = -15.38083152 x = -15.38083152 Simplifying x = -15.38083152Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.38083152, -15.38083152}
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