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Simplifying x(x + -3) = (x + 2) Reorder the terms: x(-3 + x) = (x + 2) (-3 * x + x * x) = (x + 2) (-3x + x2) = (x + 2) Reorder the terms: -3x + x2 = (2 + x) Remove parenthesis around (2 + x) -3x + x2 = 2 + x Solving -3x + x2 = 2 + x Solving for variable 'x'. Reorder the terms: -2 + -3x + -1x + x2 = 2 + x + -2 + -1x Combine like terms: -3x + -1x = -4x -2 + -4x + x2 = 2 + x + -2 + -1x Reorder the terms: -2 + -4x + x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -2 + -4x + x2 = 0 + x + -1x -2 + -4x + x2 = x + -1x Combine like terms: x + -1x = 0 -2 + -4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2' to each side of the equation. -2 + -4x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + -4x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -4x + x2 = 0 + 2 -4x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 -4x + x2 = 2 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 = 2 + 4 Reorder the terms: 4 + -4x + x2 = 2 + 4 Combine like terms: 2 + 4 = 6 4 + -4x + x2 = 6 Factor a perfect square on the left side: (x + -2)(x + -2) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -2) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -2 = 2.449489743 Simplifying x + -2 = 2.449489743 Reorder the terms: -2 + x = 2.449489743 Solving -2 + x = 2.449489743 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 = 2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x = 2.449489743 + 2 x = 2.449489743 + 2 Combine like terms: 2.449489743 + 2 = 4.449489743 x = 4.449489743 Simplifying x = 4.449489743Subproblem 2
x + -2 = -2.449489743 Simplifying x + -2 = -2.449489743 Reorder the terms: -2 + x = -2.449489743 Solving -2 + x = -2.449489743 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 = -2.449489743 + 2 Combine like terms: -2 + 2 = 0 0 + x = -2.449489743 + 2 x = -2.449489743 + 2 Combine like terms: -2.449489743 + 2 = -0.449489743 x = -0.449489743 Simplifying x = -0.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.449489743, -0.449489743}
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