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Simplifying (x + 3)(x + -3) + 12 = 8x Reorder the terms: (3 + x)(x + -3) + 12 = 8x Reorder the terms: (3 + x)(-3 + x) + 12 = 8x Multiply (3 + x) * (-3 + x) (3(-3 + x) + x(-3 + x)) + 12 = 8x ((-3 * 3 + x * 3) + x(-3 + x)) + 12 = 8x ((-9 + 3x) + x(-3 + x)) + 12 = 8x (-9 + 3x + (-3 * x + x * x)) + 12 = 8x (-9 + 3x + (-3x + x2)) + 12 = 8x Combine like terms: 3x + -3x = 0 (-9 + 0 + x2) + 12 = 8x (-9 + x2) + 12 = 8x Reorder the terms: -9 + 12 + x2 = 8x Combine like terms: -9 + 12 = 3 3 + x2 = 8x Solving 3 + x2 = 8x Solving for variable 'x'. Reorder the terms: 3 + -8x + x2 = 8x + -8x Combine like terms: 8x + -8x = 0 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}
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