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Simplifying (x + -2) + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: (-2 + x) + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Remove parenthesis around (-2 + x) -2 + x + x(x + -3) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: -2 + x + x(-3 + x) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 -2 + x + (-3 * x + x * x) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 -2 + x + (-3x + x2) = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Combine like terms: x + -3x = -2x -2 + -2x + x2 = 3(x + 4)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: -2 + -2x + x2 = 3(4 + x)(x + -3) + -1(x + 2)(x + -1) + 2 Reorder the terms: -2 + -2x + x2 = 3(4 + x)(-3 + x) + -1(x + 2)(x + -1) + 2 Multiply (4 + x) * (-3 + x) -2 + -2x + x2 = 3(4(-3 + x) + x(-3 + x)) + -1(x + 2)(x + -1) + 2 -2 + -2x + x2 = 3((-3 * 4 + x * 4) + x(-3 + x)) + -1(x + 2)(x + -1) + 2 -2 + -2x + x2 = 3((-12 + 4x) + x(-3 + x)) + -1(x + 2)(x + -1) + 2 -2 + -2x + x2 = 3(-12 + 4x + (-3 * x + x * x)) + -1(x + 2)(x + -1) + 2 -2 + -2x + x2 = 3(-12 + 4x + (-3x + x2)) + -1(x + 2)(x + -1) + 2 Combine like terms: 4x + -3x = 1x -2 + -2x + x2 = 3(-12 + 1x + x2) + -1(x + 2)(x + -1) + 2 -2 + -2x + x2 = (-12 * 3 + 1x * 3 + x2 * 3) + -1(x + 2)(x + -1) + 2 -2 + -2x + x2 = (-36 + 3x + 3x2) + -1(x + 2)(x + -1) + 2 Reorder the terms: -2 + -2x + x2 = -36 + 3x + 3x2 + -1(2 + x)(x + -1) + 2 Reorder the terms: -2 + -2x + x2 = -36 + 3x + 3x2 + -1(2 + x)(-1 + x) + 2 Multiply (2 + x) * (-1 + x) -2 + -2x + x2 = -36 + 3x + 3x2 + -1(2(-1 + x) + x(-1 + x)) + 2 -2 + -2x + x2 = -36 + 3x + 3x2 + -1((-1 * 2 + x * 2) + x(-1 + x)) + 2 -2 + -2x + x2 = -36 + 3x + 3x2 + -1((-2 + 2x) + x(-1 + x)) + 2 -2 + -2x + x2 = -36 + 3x + 3x2 + -1(-2 + 2x + (-1 * x + x * x)) + 2 -2 + -2x + x2 = -36 + 3x + 3x2 + -1(-2 + 2x + (-1x + x2)) + 2 Combine like terms: 2x + -1x = 1x -2 + -2x + x2 = -36 + 3x + 3x2 + -1(-2 + 1x + x2) + 2 -2 + -2x + x2 = -36 + 3x + 3x2 + (-2 * -1 + 1x * -1 + x2 * -1) + 2 -2 + -2x + x2 = -36 + 3x + 3x2 + (2 + -1x + -1x2) + 2 Reorder the terms: -2 + -2x + x2 = -36 + 2 + 2 + 3x + -1x + 3x2 + -1x2 Combine like terms: -36 + 2 = -34 -2 + -2x + x2 = -34 + 2 + 3x + -1x + 3x2 + -1x2 Combine like terms: -34 + 2 = -32 -2 + -2x + x2 = -32 + 3x + -1x + 3x2 + -1x2 Combine like terms: 3x + -1x = 2x -2 + -2x + x2 = -32 + 2x + 3x2 + -1x2 Combine like terms: 3x2 + -1x2 = 2x2 -2 + -2x + x2 = -32 + 2x + 2x2 Solving -2 + -2x + x2 = -32 + 2x + 2x2 Solving for variable 'x'. Reorder the terms: -2 + 32 + -2x + -2x + x2 + -2x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Combine like terms: -2 + 32 = 30 30 + -2x + -2x + x2 + -2x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Combine like terms: -2x + -2x = -4x 30 + -4x + x2 + -2x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Combine like terms: x2 + -2x2 = -1x2 30 + -4x + -1x2 = -32 + 2x + 2x2 + 32 + -2x + -2x2 Reorder the terms: 30 + -4x + -1x2 = -32 + 32 + 2x + -2x + 2x2 + -2x2 Combine like terms: -32 + 32 = 0 30 + -4x + -1x2 = 0 + 2x + -2x + 2x2 + -2x2 30 + -4x + -1x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 30 + -4x + -1x2 = 0 + 2x2 + -2x2 30 + -4x + -1x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 30 + -4x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -30 + 4x + x2 = 0 Move the constant term to the right: Add '30' to each side of the equation. -30 + 4x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 4x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 4x + x2 = 0 + 30 4x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 4x + x2 = 30 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 = 30 + 4 Reorder the terms: 4 + 4x + x2 = 30 + 4 Combine like terms: 30 + 4 = 34 4 + 4x + x2 = 34 Factor a perfect square on the left side: (x + 2)(x + 2) = 34 Calculate the square root of the right side: 5.830951895 Break this problem into two subproblems by setting (x + 2) equal to 5.830951895 and -5.830951895.Subproblem 1
x + 2 = 5.830951895 Simplifying x + 2 = 5.830951895 Reorder the terms: 2 + x = 5.830951895 Solving 2 + x = 5.830951895 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 = 5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + x = 5.830951895 + -2 x = 5.830951895 + -2 Combine like terms: 5.830951895 + -2 = 3.830951895 x = 3.830951895 Simplifying x = 3.830951895Subproblem 2
x + 2 = -5.830951895 Simplifying x + 2 = -5.830951895 Reorder the terms: 2 + x = -5.830951895 Solving 2 + x = -5.830951895 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 = -5.830951895 + -2 Combine like terms: 2 + -2 = 0 0 + x = -5.830951895 + -2 x = -5.830951895 + -2 Combine like terms: -5.830951895 + -2 = -7.830951895 x = -7.830951895 Simplifying x = -7.830951895Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.830951895, -7.830951895}
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