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Simplifying 2x2 + -12 + 2x = x * x + -2 * 2 + 2 Reorder the terms: -12 + 2x + 2x2 = x * x + -2 * 2 + 2 Multiply x * x -12 + 2x + 2x2 = x2 + -2 * 2 + 2 Multiply -2 * 2 -12 + 2x + 2x2 = x2 + -4 + 2 Reorder the terms: -12 + 2x + 2x2 = -4 + 2 + x2 Combine like terms: -4 + 2 = -2 -12 + 2x + 2x2 = -2 + x2 Solving -12 + 2x + 2x2 = -2 + x2 Solving for variable 'x'. Reorder the terms: -12 + 2 + 2x + 2x2 + -1x2 = -2 + x2 + 2 + -1x2 Combine like terms: -12 + 2 = -10 -10 + 2x + 2x2 + -1x2 = -2 + x2 + 2 + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -10 + 2x + 1x2 = -2 + x2 + 2 + -1x2 Reorder the terms: -10 + 2x + 1x2 = -2 + 2 + x2 + -1x2 Combine like terms: -2 + 2 = 0 -10 + 2x + 1x2 = 0 + x2 + -1x2 -10 + 2x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -10 + 2x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '10' to each side of the equation. -10 + 2x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 2x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 2x + x2 = 0 + 10 2x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 2x + x2 = 10 The x term is 2x. Take half its coefficient (1). Square it (1) and add it to both sides. Add '1' to each side of the equation. 2x + 1 + x2 = 10 + 1 Reorder the terms: 1 + 2x + x2 = 10 + 1 Combine like terms: 10 + 1 = 11 1 + 2x + x2 = 11 Factor a perfect square on the left side: (x + 1)(x + 1) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + 1) equal to 3.31662479 and -3.31662479.Subproblem 1
x + 1 = 3.31662479 Simplifying x + 1 = 3.31662479 Reorder the terms: 1 + x = 3.31662479 Solving 1 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = 3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = 3.31662479 + -1 x = 3.31662479 + -1 Combine like terms: 3.31662479 + -1 = 2.31662479 x = 2.31662479 Simplifying x = 2.31662479Subproblem 2
x + 1 = -3.31662479 Simplifying x + 1 = -3.31662479 Reorder the terms: 1 + x = -3.31662479 Solving 1 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + x = -3.31662479 + -1 Combine like terms: 1 + -1 = 0 0 + x = -3.31662479 + -1 x = -3.31662479 + -1 Combine like terms: -3.31662479 + -1 = -4.31662479 x = -4.31662479 Simplifying x = -4.31662479Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.31662479, -4.31662479}
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