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Simplifying (2x + -1)(2x + -1) + -1(x + 2)(3x + -2) = 0 Reorder the terms: (-1 + 2x)(2x + -1) + -1(x + 2)(3x + -2) = 0 Reorder the terms: (-1 + 2x)(-1 + 2x) + -1(x + 2)(3x + -2) = 0 Multiply (-1 + 2x) * (-1 + 2x) (-1(-1 + 2x) + 2x * (-1 + 2x)) + -1(x + 2)(3x + -2) = 0 ((-1 * -1 + 2x * -1) + 2x * (-1 + 2x)) + -1(x + 2)(3x + -2) = 0 ((1 + -2x) + 2x * (-1 + 2x)) + -1(x + 2)(3x + -2) = 0 (1 + -2x + (-1 * 2x + 2x * 2x)) + -1(x + 2)(3x + -2) = 0 (1 + -2x + (-2x + 4x2)) + -1(x + 2)(3x + -2) = 0 Combine like terms: -2x + -2x = -4x (1 + -4x + 4x2) + -1(x + 2)(3x + -2) = 0 Reorder the terms: 1 + -4x + 4x2 + -1(2 + x)(3x + -2) = 0 Reorder the terms: 1 + -4x + 4x2 + -1(2 + x)(-2 + 3x) = 0 Multiply (2 + x) * (-2 + 3x) 1 + -4x + 4x2 + -1(2(-2 + 3x) + x(-2 + 3x)) = 0 1 + -4x + 4x2 + -1((-2 * 2 + 3x * 2) + x(-2 + 3x)) = 0 1 + -4x + 4x2 + -1((-4 + 6x) + x(-2 + 3x)) = 0 1 + -4x + 4x2 + -1(-4 + 6x + (-2 * x + 3x * x)) = 0 1 + -4x + 4x2 + -1(-4 + 6x + (-2x + 3x2)) = 0 Combine like terms: 6x + -2x = 4x 1 + -4x + 4x2 + -1(-4 + 4x + 3x2) = 0 1 + -4x + 4x2 + (-4 * -1 + 4x * -1 + 3x2 * -1) = 0 1 + -4x + 4x2 + (4 + -4x + -3x2) = 0 Reorder the terms: 1 + 4 + -4x + -4x + 4x2 + -3x2 = 0 Combine like terms: 1 + 4 = 5 5 + -4x + -4x + 4x2 + -3x2 = 0 Combine like terms: -4x + -4x = -8x 5 + -8x + 4x2 + -3x2 = 0 Combine like terms: 4x2 + -3x2 = 1x2 5 + -8x + 1x2 = 0 Solving 5 + -8x + 1x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-5' to each side of the equation. 5 + -8x + -5 + x2 = 0 + -5 Reorder the terms: 5 + -5 + -8x + x2 = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -8x + x2 = 0 + -5 -8x + x2 = 0 + -5 Combine like terms: 0 + -5 = -5 -8x + x2 = -5 The x term is -8x. Take half its coefficient (-4). Square it (16) and add it to both sides. Add '16' to each side of the equation. -8x + 16 + x2 = -5 + 16 Reorder the terms: 16 + -8x + x2 = -5 + 16 Combine like terms: -5 + 16 = 11 16 + -8x + x2 = 11 Factor a perfect square on the left side: (x + -4)(x + -4) = 11 Calculate the square root of the right side: 3.31662479 Break this problem into two subproblems by setting (x + -4) equal to 3.31662479 and -3.31662479.Subproblem 1
x + -4 = 3.31662479 Simplifying x + -4 = 3.31662479 Reorder the terms: -4 + x = 3.31662479 Solving -4 + x = 3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = 3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.31662479 + 4 x = 3.31662479 + 4 Combine like terms: 3.31662479 + 4 = 7.31662479 x = 7.31662479 Simplifying x = 7.31662479Subproblem 2
x + -4 = -3.31662479 Simplifying x + -4 = -3.31662479 Reorder the terms: -4 + x = -3.31662479 Solving -4 + x = -3.31662479 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + x = -3.31662479 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.31662479 + 4 x = -3.31662479 + 4 Combine like terms: -3.31662479 + 4 = 0.68337521 x = 0.68337521 Simplifying x = 0.68337521Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.31662479, 0.68337521}
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