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Simplifying (2x + -3)(x + 1) = (x + -3)(x + -2) Reorder the terms: (-3 + 2x)(x + 1) = (x + -3)(x + -2) Reorder the terms: (-3 + 2x)(1 + x) = (x + -3)(x + -2) Multiply (-3 + 2x) * (1 + x) (-3(1 + x) + 2x * (1 + x)) = (x + -3)(x + -2) ((1 * -3 + x * -3) + 2x * (1 + x)) = (x + -3)(x + -2) ((-3 + -3x) + 2x * (1 + x)) = (x + -3)(x + -2) (-3 + -3x + (1 * 2x + x * 2x)) = (x + -3)(x + -2) (-3 + -3x + (2x + 2x2)) = (x + -3)(x + -2) Combine like terms: -3x + 2x = -1x (-3 + -1x + 2x2) = (x + -3)(x + -2) Reorder the terms: -3 + -1x + 2x2 = (-3 + x)(x + -2) Reorder the terms: -3 + -1x + 2x2 = (-3 + x)(-2 + x) Multiply (-3 + x) * (-2 + x) -3 + -1x + 2x2 = (-3(-2 + x) + x(-2 + x)) -3 + -1x + 2x2 = ((-2 * -3 + x * -3) + x(-2 + x)) -3 + -1x + 2x2 = ((6 + -3x) + x(-2 + x)) -3 + -1x + 2x2 = (6 + -3x + (-2 * x + x * x)) -3 + -1x + 2x2 = (6 + -3x + (-2x + x2)) Combine like terms: -3x + -2x = -5x -3 + -1x + 2x2 = (6 + -5x + x2) Solving -3 + -1x + 2x2 = 6 + -5x + x2 Solving for variable 'x'. Reorder the terms: -3 + -6 + -1x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Combine like terms: -3 + -6 = -9 -9 + -1x + 5x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Combine like terms: -1x + 5x = 4x -9 + 4x + 2x2 + -1x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Combine like terms: 2x2 + -1x2 = 1x2 -9 + 4x + 1x2 = 6 + -5x + x2 + -6 + 5x + -1x2 Reorder the terms: -9 + 4x + 1x2 = 6 + -6 + -5x + 5x + x2 + -1x2 Combine like terms: 6 + -6 = 0 -9 + 4x + 1x2 = 0 + -5x + 5x + x2 + -1x2 -9 + 4x + 1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 -9 + 4x + 1x2 = 0 + x2 + -1x2 -9 + 4x + 1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -9 + 4x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 4x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 4x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4x + x2 = 0 + 9 4x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 4x + x2 = 9 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 = 9 + 4 Reorder the terms: 4 + 4x + x2 = 9 + 4 Combine like terms: 9 + 4 = 13 4 + 4x + x2 = 13 Factor a perfect square on the left side: (x + 2)(x + 2) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + 2) equal to 3.605551275 and -3.605551275.Subproblem 1
x + 2 = 3.605551275 Simplifying x + 2 = 3.605551275 Reorder the terms: 2 + x = 3.605551275 Solving 2 + x = 3.605551275 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 = 3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = 3.605551275 + -2 x = 3.605551275 + -2 Combine like terms: 3.605551275 + -2 = 1.605551275 x = 1.605551275 Simplifying x = 1.605551275Subproblem 2
x + 2 = -3.605551275 Simplifying x + 2 = -3.605551275 Reorder the terms: 2 + x = -3.605551275 Solving 2 + x = -3.605551275 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 = -3.605551275 + -2 Combine like terms: 2 + -2 = 0 0 + x = -3.605551275 + -2 x = -3.605551275 + -2 Combine like terms: -3.605551275 + -2 = -5.605551275 x = -5.605551275 Simplifying x = -5.605551275Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.605551275, -5.605551275}
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