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Simplifying x2 + -6x + -6x + -12 = 7 Reorder the terms: -12 + -6x + -6x + x2 = 7 Combine like terms: -6x + -6x = -12x -12 + -12x + x2 = 7 Solving -12 + -12x + x2 = 7 Solving for variable 'x'. Reorder the terms: -12 + -7 + -12x + x2 = 7 + -7 Combine like terms: -12 + -7 = -19 -19 + -12x + x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -19 + -12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -12x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -12x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -12x + x2 = 0 + 19 -12x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -12x + x2 = 19 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 = 19 + 36 Reorder the terms: 36 + -12x + x2 = 19 + 36 Combine like terms: 19 + 36 = 55 36 + -12x + x2 = 55 Factor a perfect square on the left side: (x + -6)(x + -6) = 55 Calculate the square root of the right side: 7.416198487 Break this problem into two subproblems by setting (x + -6) equal to 7.416198487 and -7.416198487.Subproblem 1
x + -6 = 7.416198487 Simplifying x + -6 = 7.416198487 Reorder the terms: -6 + x = 7.416198487 Solving -6 + x = 7.416198487 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 = 7.416198487 + 6 Combine like terms: -6 + 6 = 0 0 + x = 7.416198487 + 6 x = 7.416198487 + 6 Combine like terms: 7.416198487 + 6 = 13.416198487 x = 13.416198487 Simplifying x = 13.416198487Subproblem 2
x + -6 = -7.416198487 Simplifying x + -6 = -7.416198487 Reorder the terms: -6 + x = -7.416198487 Solving -6 + x = -7.416198487 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 = -7.416198487 + 6 Combine like terms: -6 + 6 = 0 0 + x = -7.416198487 + 6 x = -7.416198487 + 6 Combine like terms: -7.416198487 + 6 = -1.416198487 x = -1.416198487 Simplifying x = -1.416198487Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.416198487, -1.416198487}
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