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Simplifying 2x2 + -6x = x(x + 6) + 4 Reorder the terms: -6x + 2x2 = x(x + 6) + 4 Reorder the terms: -6x + 2x2 = x(6 + x) + 4 -6x + 2x2 = (6 * x + x * x) + 4 -6x + 2x2 = (6x + x2) + 4 Reorder the terms: -6x + 2x2 = 4 + 6x + x2 Solving -6x + 2x2 = 4 + 6x + x2 Solving for variable 'x'. Reorder the terms: -4 + -6x + -6x + 2x2 + -1x2 = 4 + 6x + x2 + -4 + -6x + -1x2 Combine like terms: -6x + -6x = -12x -4 + -12x + 2x2 + -1x2 = 4 + 6x + x2 + -4 + -6x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -4 + -12x + 1x2 = 4 + 6x + x2 + -4 + -6x + -1x2 Reorder the terms: -4 + -12x + 1x2 = 4 + -4 + 6x + -6x + x2 + -1x2 Combine like terms: 4 + -4 = 0 -4 + -12x + 1x2 = 0 + 6x + -6x + x2 + -1x2 -4 + -12x + 1x2 = 6x + -6x + x2 + -1x2 Combine like terms: 6x + -6x = 0 -4 + -12x + 1x2 = 0 + x2 + -1x2 -4 + -12x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -4 + -12x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + -12x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -12x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -12x + x2 = 0 + 4 -12x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -12x + x2 = 4 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 = 4 + 36 Reorder the terms: 36 + -12x + x2 = 4 + 36 Combine like terms: 4 + 36 = 40 36 + -12x + x2 = 40 Factor a perfect square on the left side: (x + -6)(x + -6) = 40 Calculate the square root of the right side: 6.32455532 Break this problem into two subproblems by setting (x + -6) equal to 6.32455532 and -6.32455532.Subproblem 1
x + -6 = 6.32455532 Simplifying x + -6 = 6.32455532 Reorder the terms: -6 + x = 6.32455532 Solving -6 + x = 6.32455532 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 = 6.32455532 + 6 Combine like terms: -6 + 6 = 0 0 + x = 6.32455532 + 6 x = 6.32455532 + 6 Combine like terms: 6.32455532 + 6 = 12.32455532 x = 12.32455532 Simplifying x = 12.32455532Subproblem 2
x + -6 = -6.32455532 Simplifying x + -6 = -6.32455532 Reorder the terms: -6 + x = -6.32455532 Solving -6 + x = -6.32455532 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 = -6.32455532 + 6 Combine like terms: -6 + 6 = 0 0 + x = -6.32455532 + 6 x = -6.32455532 + 6 Combine like terms: -6.32455532 + 6 = -0.32455532 x = -0.32455532 Simplifying x = -0.32455532Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.32455532, -0.32455532}
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