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Simplifying 3(x + -2)(x + 1) + -4 = 2x2 + -2 Reorder the terms: 3(-2 + x)(x + 1) + -4 = 2x2 + -2 Reorder the terms: 3(-2 + x)(1 + x) + -4 = 2x2 + -2 Multiply (-2 + x) * (1 + x) 3(-2(1 + x) + x(1 + x)) + -4 = 2x2 + -2 3((1 * -2 + x * -2) + x(1 + x)) + -4 = 2x2 + -2 3((-2 + -2x) + x(1 + x)) + -4 = 2x2 + -2 3(-2 + -2x + (1 * x + x * x)) + -4 = 2x2 + -2 3(-2 + -2x + (1x + x2)) + -4 = 2x2 + -2 Combine like terms: -2x + 1x = -1x 3(-2 + -1x + x2) + -4 = 2x2 + -2 (-2 * 3 + -1x * 3 + x2 * 3) + -4 = 2x2 + -2 (-6 + -3x + 3x2) + -4 = 2x2 + -2 Reorder the terms: -6 + -4 + -3x + 3x2 = 2x2 + -2 Combine like terms: -6 + -4 = -10 -10 + -3x + 3x2 = 2x2 + -2 Reorder the terms: -10 + -3x + 3x2 = -2 + 2x2 Solving -10 + -3x + 3x2 = -2 + 2x2 Solving for variable 'x'. Reorder the terms: -10 + 2 + -3x + 3x2 + -2x2 = -2 + 2x2 + 2 + -2x2 Combine like terms: -10 + 2 = -8 -8 + -3x + 3x2 + -2x2 = -2 + 2x2 + 2 + -2x2 Combine like terms: 3x2 + -2x2 = 1x2 -8 + -3x + 1x2 = -2 + 2x2 + 2 + -2x2 Reorder the terms: -8 + -3x + 1x2 = -2 + 2 + 2x2 + -2x2 Combine like terms: -2 + 2 = 0 -8 + -3x + 1x2 = 0 + 2x2 + -2x2 -8 + -3x + 1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 -8 + -3x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '8' to each side of the equation. -8 + -3x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + -3x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + -3x + x2 = 0 + 8 -3x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 -3x + x2 = 8 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 8 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 8 + 2.25 Combine like terms: 8 + 2.25 = 10.25 2.25 + -3x + x2 = 10.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 10.25 Calculate the square root of the right side: 3.201562119 Break this problem into two subproblems by setting (x + -1.5) equal to 3.201562119 and -3.201562119.Subproblem 1
x + -1.5 = 3.201562119 Simplifying x + -1.5 = 3.201562119 Reorder the terms: -1.5 + x = 3.201562119 Solving -1.5 + x = 3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 3.201562119 + 1.5 x = 3.201562119 + 1.5 Combine like terms: 3.201562119 + 1.5 = 4.701562119 x = 4.701562119 Simplifying x = 4.701562119Subproblem 2
x + -1.5 = -3.201562119 Simplifying x + -1.5 = -3.201562119 Reorder the terms: -1.5 + x = -3.201562119 Solving -1.5 + x = -3.201562119 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -3.201562119 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -3.201562119 + 1.5 x = -3.201562119 + 1.5 Combine like terms: -3.201562119 + 1.5 = -1.701562119 x = -1.701562119 Simplifying x = -1.701562119Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.701562119, -1.701562119}
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