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Simplifying (3x + -2)(x + 5) = (2 + x) Reorder the terms: (-2 + 3x)(x + 5) = (2 + x) Reorder the terms: (-2 + 3x)(5 + x) = (2 + x) Multiply (-2 + 3x) * (5 + x) (-2(5 + x) + 3x * (5 + x)) = (2 + x) ((5 * -2 + x * -2) + 3x * (5 + x)) = (2 + x) ((-10 + -2x) + 3x * (5 + x)) = (2 + x) (-10 + -2x + (5 * 3x + x * 3x)) = (2 + x) (-10 + -2x + (15x + 3x2)) = (2 + x) Combine like terms: -2x + 15x = 13x (-10 + 13x + 3x2) = (2 + x) Remove parenthesis around (2 + x) -10 + 13x + 3x2 = 2 + x Solving -10 + 13x + 3x2 = 2 + x Solving for variable 'x'. Reorder the terms: -10 + -2 + 13x + -1x + 3x2 = 2 + x + -2 + -1x Combine like terms: -10 + -2 = -12 -12 + 13x + -1x + 3x2 = 2 + x + -2 + -1x Combine like terms: 13x + -1x = 12x -12 + 12x + 3x2 = 2 + x + -2 + -1x Reorder the terms: -12 + 12x + 3x2 = 2 + -2 + x + -1x Combine like terms: 2 + -2 = 0 -12 + 12x + 3x2 = 0 + x + -1x -12 + 12x + 3x2 = x + -1x Combine like terms: x + -1x = 0 -12 + 12x + 3x2 = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-4 + 4x + x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-4 + 4x + x2)' equal to zero and attempt to solve: Simplifying -4 + 4x + x2 = 0 Solving -4 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '4' to each side of the equation. -4 + 4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + 4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 4x + x2 = 0 + 4 4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 4x + x2 = 4 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 = 4 + 4 Reorder the terms: 4 + 4x + x2 = 4 + 4 Combine like terms: 4 + 4 = 8 4 + 4x + x2 = 8 Factor a perfect square on the left side: (x + 2)(x + 2) = 8 Calculate the square root of the right side: 2.828427125 Break this problem into two subproblems by setting (x + 2) equal to 2.828427125 and -2.828427125.Subproblem 1
x + 2 = 2.828427125 Simplifying x + 2 = 2.828427125 Reorder the terms: 2 + x = 2.828427125 Solving 2 + x = 2.828427125 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 = 2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = 2.828427125 + -2 x = 2.828427125 + -2 Combine like terms: 2.828427125 + -2 = 0.828427125 x = 0.828427125 Simplifying x = 0.828427125Subproblem 2
x + 2 = -2.828427125 Simplifying x + 2 = -2.828427125 Reorder the terms: 2 + x = -2.828427125 Solving 2 + x = -2.828427125 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 = -2.828427125 + -2 Combine like terms: 2 + -2 = 0 0 + x = -2.828427125 + -2 x = -2.828427125 + -2 Combine like terms: -2.828427125 + -2 = -4.828427125 x = -4.828427125 Simplifying x = -4.828427125Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.828427125, -4.828427125}Solution
x = {0.828427125, -4.828427125}
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