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Simplifying x * x + 6x + -5 = 12 Multiply x * x x2 + 6x + -5 = 12 Reorder the terms: -5 + 6x + x2 = 12 Solving -5 + 6x + x2 = 12 Solving for variable 'x'. Reorder the terms: -5 + -12 + 6x + x2 = 12 + -12 Combine like terms: -5 + -12 = -17 -17 + 6x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -17 + 6x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '17' to each side of the equation. -17 + 6x + 17 + x2 = 0 + 17 Reorder the terms: -17 + 17 + 6x + x2 = 0 + 17 Combine like terms: -17 + 17 = 0 0 + 6x + x2 = 0 + 17 6x + x2 = 0 + 17 Combine like terms: 0 + 17 = 17 6x + x2 = 17 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 = 17 + 9 Reorder the terms: 9 + 6x + x2 = 17 + 9 Combine like terms: 17 + 9 = 26 9 + 6x + x2 = 26 Factor a perfect square on the left side: (x + 3)(x + 3) = 26 Calculate the square root of the right side: 5.099019514 Break this problem into two subproblems by setting (x + 3) equal to 5.099019514 and -5.099019514.Subproblem 1
x + 3 = 5.099019514 Simplifying x + 3 = 5.099019514 Reorder the terms: 3 + x = 5.099019514 Solving 3 + x = 5.099019514 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 = 5.099019514 + -3 Combine like terms: 3 + -3 = 0 0 + x = 5.099019514 + -3 x = 5.099019514 + -3 Combine like terms: 5.099019514 + -3 = 2.099019514 x = 2.099019514 Simplifying x = 2.099019514Subproblem 2
x + 3 = -5.099019514 Simplifying x + 3 = -5.099019514 Reorder the terms: 3 + x = -5.099019514 Solving 3 + x = -5.099019514 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 = -5.099019514 + -3 Combine like terms: 3 + -3 = 0 0 + x = -5.099019514 + -3 x = -5.099019514 + -3 Combine like terms: -5.099019514 + -3 = -8.099019514 x = -8.099019514 Simplifying x = -8.099019514Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.099019514, -8.099019514}
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