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Simplifying 2x(x + -6) + 2 = 4x + -4 Reorder the terms: 2x(-6 + x) + 2 = 4x + -4 (-6 * 2x + x * 2x) + 2 = 4x + -4 (-12x + 2x2) + 2 = 4x + -4 Reorder the terms: 2 + -12x + 2x2 = 4x + -4 Reorder the terms: 2 + -12x + 2x2 = -4 + 4x Solving 2 + -12x + 2x2 = -4 + 4x Solving for variable 'x'. Reorder the terms: 2 + 4 + -12x + -4x + 2x2 = -4 + 4x + 4 + -4x Combine like terms: 2 + 4 = 6 6 + -12x + -4x + 2x2 = -4 + 4x + 4 + -4x Combine like terms: -12x + -4x = -16x 6 + -16x + 2x2 = -4 + 4x + 4 + -4x Reorder the terms: 6 + -16x + 2x2 = -4 + 4 + 4x + -4x Combine like terms: -4 + 4 = 0 6 + -16x + 2x2 = 0 + 4x + -4x 6 + -16x + 2x2 = 4x + -4x Combine like terms: 4x + -4x = 0 6 + -16x + 2x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(3 + -8x + x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(3 + -8x + x2)' equal to zero and attempt to solve: Simplifying 3 + -8x + x2 = 0 Solving 3 + -8x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-3' to each side of the equation. 3 + -8x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -8x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -8x + x2 = 0 + -3 -8x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -8x + x2 = -3 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 = -3 + 16 Reorder the terms: 16 + -8x + x2 = -3 + 16 Combine like terms: -3 + 16 = 13 16 + -8x + x2 = 13 Factor a perfect square on the left side: (x + -4)(x + -4) = 13 Calculate the square root of the right side: 3.605551275 Break this problem into two subproblems by setting (x + -4) equal to 3.605551275 and -3.605551275.Subproblem 1
x + -4 = 3.605551275 Simplifying x + -4 = 3.605551275 Reorder the terms: -4 + x = 3.605551275 Solving -4 + x = 3.605551275 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 = 3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x = 3.605551275 + 4 x = 3.605551275 + 4 Combine like terms: 3.605551275 + 4 = 7.605551275 x = 7.605551275 Simplifying x = 7.605551275Subproblem 2
x + -4 = -3.605551275 Simplifying x + -4 = -3.605551275 Reorder the terms: -4 + x = -3.605551275 Solving -4 + x = -3.605551275 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 = -3.605551275 + 4 Combine like terms: -4 + 4 = 0 0 + x = -3.605551275 + 4 x = -3.605551275 + 4 Combine like terms: -3.605551275 + 4 = 0.394448725 x = 0.394448725 Simplifying x = 0.394448725Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.605551275, 0.394448725}Solution
x = {7.605551275, 0.394448725}
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