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Simplifying 3x + 9 = (8x + 2)(x + -6) Reorder the terms: 9 + 3x = (8x + 2)(x + -6) Reorder the terms: 9 + 3x = (2 + 8x)(x + -6) Reorder the terms: 9 + 3x = (2 + 8x)(-6 + x) Multiply (2 + 8x) * (-6 + x) 9 + 3x = (2(-6 + x) + 8x * (-6 + x)) 9 + 3x = ((-6 * 2 + x * 2) + 8x * (-6 + x)) 9 + 3x = ((-12 + 2x) + 8x * (-6 + x)) 9 + 3x = (-12 + 2x + (-6 * 8x + x * 8x)) 9 + 3x = (-12 + 2x + (-48x + 8x2)) Combine like terms: 2x + -48x = -46x 9 + 3x = (-12 + -46x + 8x2) Solving 9 + 3x = -12 + -46x + 8x2 Solving for variable 'x'. Reorder the terms: 9 + 12 + 3x + 46x + -8x2 = -12 + -46x + 8x2 + 12 + 46x + -8x2 Combine like terms: 9 + 12 = 21 21 + 3x + 46x + -8x2 = -12 + -46x + 8x2 + 12 + 46x + -8x2 Combine like terms: 3x + 46x = 49x 21 + 49x + -8x2 = -12 + -46x + 8x2 + 12 + 46x + -8x2 Reorder the terms: 21 + 49x + -8x2 = -12 + 12 + -46x + 46x + 8x2 + -8x2 Combine like terms: -12 + 12 = 0 21 + 49x + -8x2 = 0 + -46x + 46x + 8x2 + -8x2 21 + 49x + -8x2 = -46x + 46x + 8x2 + -8x2 Combine like terms: -46x + 46x = 0 21 + 49x + -8x2 = 0 + 8x2 + -8x2 21 + 49x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 21 + 49x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -2.625 + -6.125x + x2 = 0 Move the constant term to the right: Add '2.625' to each side of the equation. -2.625 + -6.125x + 2.625 + x2 = 0 + 2.625 Reorder the terms: -2.625 + 2.625 + -6.125x + x2 = 0 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + -6.125x + x2 = 0 + 2.625 -6.125x + x2 = 0 + 2.625 Combine like terms: 0 + 2.625 = 2.625 -6.125x + x2 = 2.625 The x term is -6.125x. Take half its coefficient (-3.0625). Square it (9.37890625) and add it to both sides. Add '9.37890625' to each side of the equation. -6.125x + 9.37890625 + x2 = 2.625 + 9.37890625 Reorder the terms: 9.37890625 + -6.125x + x2 = 2.625 + 9.37890625 Combine like terms: 2.625 + 9.37890625 = 12.00390625 9.37890625 + -6.125x + x2 = 12.00390625 Factor a perfect square on the left side: (x + -3.0625)(x + -3.0625) = 12.00390625 Calculate the square root of the right side: 3.464665388 Break this problem into two subproblems by setting (x + -3.0625) equal to 3.464665388 and -3.464665388.Subproblem 1
x + -3.0625 = 3.464665388 Simplifying x + -3.0625 = 3.464665388 Reorder the terms: -3.0625 + x = 3.464665388 Solving -3.0625 + x = 3.464665388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = 3.464665388 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = 3.464665388 + 3.0625 x = 3.464665388 + 3.0625 Combine like terms: 3.464665388 + 3.0625 = 6.527165388 x = 6.527165388 Simplifying x = 6.527165388Subproblem 2
x + -3.0625 = -3.464665388 Simplifying x + -3.0625 = -3.464665388 Reorder the terms: -3.0625 + x = -3.464665388 Solving -3.0625 + x = -3.464665388 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.0625' to each side of the equation. -3.0625 + 3.0625 + x = -3.464665388 + 3.0625 Combine like terms: -3.0625 + 3.0625 = 0.0000 0.0000 + x = -3.464665388 + 3.0625 x = -3.464665388 + 3.0625 Combine like terms: -3.464665388 + 3.0625 = -0.402165388 x = -0.402165388 Simplifying x = -0.402165388Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.527165388, -0.402165388}
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