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Simplifying x2 + -4x + 4 + -11 = 12 Reorder the terms: 4 + -11 + -4x + x2 = 12 Combine like terms: 4 + -11 = -7 -7 + -4x + x2 = 12 Solving -7 + -4x + x2 = 12 Solving for variable 'x'. Reorder the terms: -7 + -12 + -4x + x2 = 12 + -12 Combine like terms: -7 + -12 = -19 -19 + -4x + x2 = 12 + -12 Combine like terms: 12 + -12 = 0 -19 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '19' to each side of the equation. -19 + -4x + 19 + x2 = 0 + 19 Reorder the terms: -19 + 19 + -4x + x2 = 0 + 19 Combine like terms: -19 + 19 = 0 0 + -4x + x2 = 0 + 19 -4x + x2 = 0 + 19 Combine like terms: 0 + 19 = 19 -4x + x2 = 19 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = 19 + 4 Reorder the terms: 4 + -4x + x2 = 19 + 4 Combine like terms: 19 + 4 = 23 4 + -4x + x2 = 23 Factor a perfect square on the left side: (x + -2)(x + -2) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + -2) equal to 4.795831523 and -4.795831523.Subproblem 1
x + -2 = 4.795831523 Simplifying x + -2 = 4.795831523 Reorder the terms: -2 + x = 4.795831523 Solving -2 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + x = 4.795831523 + 2 x = 4.795831523 + 2 Combine like terms: 4.795831523 + 2 = 6.795831523 x = 6.795831523 Simplifying x = 6.795831523Subproblem 2
x + -2 = -4.795831523 Simplifying x + -2 = -4.795831523 Reorder the terms: -2 + x = -4.795831523 Solving -2 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -4.795831523 + 2 Combine like terms: -2 + 2 = 0 0 + x = -4.795831523 + 2 x = -4.795831523 + 2 Combine like terms: -4.795831523 + 2 = -2.795831523 x = -2.795831523 Simplifying x = -2.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.795831523, -2.795831523}
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