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Simplifying 3x + -1(-2x + 6) = 4 + -2x(x + -4) + x Reorder the terms: 3x + -1(6 + -2x) = 4 + -2x(x + -4) + x 3x + (6 * -1 + -2x * -1) = 4 + -2x(x + -4) + x 3x + (-6 + 2x) = 4 + -2x(x + -4) + x Reorder the terms: -6 + 3x + 2x = 4 + -2x(x + -4) + x Combine like terms: 3x + 2x = 5x -6 + 5x = 4 + -2x(x + -4) + x Reorder the terms: -6 + 5x = 4 + -2x(-4 + x) + x -6 + 5x = 4 + (-4 * -2x + x * -2x) + x -6 + 5x = 4 + (8x + -2x2) + x Reorder the terms: -6 + 5x = 4 + 8x + x + -2x2 Combine like terms: 8x + x = 9x -6 + 5x = 4 + 9x + -2x2 Solving -6 + 5x = 4 + 9x + -2x2 Solving for variable 'x'. Reorder the terms: -6 + -4 + 5x + -9x + 2x2 = 4 + 9x + -2x2 + -4 + -9x + 2x2 Combine like terms: -6 + -4 = -10 -10 + 5x + -9x + 2x2 = 4 + 9x + -2x2 + -4 + -9x + 2x2 Combine like terms: 5x + -9x = -4x -10 + -4x + 2x2 = 4 + 9x + -2x2 + -4 + -9x + 2x2 Reorder the terms: -10 + -4x + 2x2 = 4 + -4 + 9x + -9x + -2x2 + 2x2 Combine like terms: 4 + -4 = 0 -10 + -4x + 2x2 = 0 + 9x + -9x + -2x2 + 2x2 -10 + -4x + 2x2 = 9x + -9x + -2x2 + 2x2 Combine like terms: 9x + -9x = 0 -10 + -4x + 2x2 = 0 + -2x2 + 2x2 -10 + -4x + 2x2 = -2x2 + 2x2 Combine like terms: -2x2 + 2x2 = 0 -10 + -4x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-5 + -2x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-5 + -2x + x2)' equal to zero and attempt to solve: Simplifying -5 + -2x + x2 = 0 Solving -5 + -2x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + -2x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -2x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2x + x2 = 0 + 5 -2x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -2x + x2 = 5 The x term is -2x. Take half its coefficient (-1). Square it (1) and add it to both sides. Add '1' to each side of the equation. -2x + 1 + x2 = 5 + 1 Reorder the terms: 1 + -2x + x2 = 5 + 1 Combine like terms: 5 + 1 = 6 1 + -2x + x2 = 6 Factor a perfect square on the left side: (x + -1)(x + -1) = 6 Calculate the square root of the right side: 2.449489743 Break this problem into two subproblems by setting (x + -1) equal to 2.449489743 and -2.449489743.Subproblem 1
x + -1 = 2.449489743 Simplifying x + -1 = 2.449489743 Reorder the terms: -1 + x = 2.449489743 Solving -1 + x = 2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = 2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = 2.449489743 + 1 x = 2.449489743 + 1 Combine like terms: 2.449489743 + 1 = 3.449489743 x = 3.449489743 Simplifying x = 3.449489743Subproblem 2
x + -1 = -2.449489743 Simplifying x + -1 = -2.449489743 Reorder the terms: -1 + x = -2.449489743 Solving -1 + x = -2.449489743 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + x = -2.449489743 + 1 Combine like terms: -1 + 1 = 0 0 + x = -2.449489743 + 1 x = -2.449489743 + 1 Combine like terms: -2.449489743 + 1 = -1.449489743 x = -1.449489743 Simplifying x = -1.449489743Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.449489743, -1.449489743}Solution
x = {3.449489743, -1.449489743}
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