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Simplifying 6x + 3 = 8x(x + -4) + 11x Reorder the terms: 3 + 6x = 8x(x + -4) + 11x Reorder the terms: 3 + 6x = 8x(-4 + x) + 11x 3 + 6x = (-4 * 8x + x * 8x) + 11x 3 + 6x = (-32x + 8x2) + 11x Reorder the terms: 3 + 6x = -32x + 11x + 8x2 Combine like terms: -32x + 11x = -21x 3 + 6x = -21x + 8x2 Solving 3 + 6x = -21x + 8x2 Solving for variable 'x'. Combine like terms: 6x + 21x = 27x 3 + 27x + -8x2 = -21x + 8x2 + 21x + -8x2 Reorder the terms: 3 + 27x + -8x2 = -21x + 21x + 8x2 + -8x2 Combine like terms: -21x + 21x = 0 3 + 27x + -8x2 = 0 + 8x2 + -8x2 3 + 27x + -8x2 = 8x2 + -8x2 Combine like terms: 8x2 + -8x2 = 0 3 + 27x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -0.375 + -3.375x + x2 = 0 Move the constant term to the right: Add '0.375' to each side of the equation. -0.375 + -3.375x + 0.375 + x2 = 0 + 0.375 Reorder the terms: -0.375 + 0.375 + -3.375x + x2 = 0 + 0.375 Combine like terms: -0.375 + 0.375 = 0.000 0.000 + -3.375x + x2 = 0 + 0.375 -3.375x + x2 = 0 + 0.375 Combine like terms: 0 + 0.375 = 0.375 -3.375x + x2 = 0.375 The x term is -3.375x. Take half its coefficient (-1.6875). Square it (2.84765625) and add it to both sides. Add '2.84765625' to each side of the equation. -3.375x + 2.84765625 + x2 = 0.375 + 2.84765625 Reorder the terms: 2.84765625 + -3.375x + x2 = 0.375 + 2.84765625 Combine like terms: 0.375 + 2.84765625 = 3.22265625 2.84765625 + -3.375x + x2 = 3.22265625 Factor a perfect square on the left side: (x + -1.6875)(x + -1.6875) = 3.22265625 Calculate the square root of the right side: 1.795175827 Break this problem into two subproblems by setting (x + -1.6875) equal to 1.795175827 and -1.795175827.Subproblem 1
x + -1.6875 = 1.795175827 Simplifying x + -1.6875 = 1.795175827 Reorder the terms: -1.6875 + x = 1.795175827 Solving -1.6875 + x = 1.795175827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = 1.795175827 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = 1.795175827 + 1.6875 x = 1.795175827 + 1.6875 Combine like terms: 1.795175827 + 1.6875 = 3.482675827 x = 3.482675827 Simplifying x = 3.482675827Subproblem 2
x + -1.6875 = -1.795175827 Simplifying x + -1.6875 = -1.795175827 Reorder the terms: -1.6875 + x = -1.795175827 Solving -1.6875 + x = -1.795175827 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.6875' to each side of the equation. -1.6875 + 1.6875 + x = -1.795175827 + 1.6875 Combine like terms: -1.6875 + 1.6875 = 0.0000 0.0000 + x = -1.795175827 + 1.6875 x = -1.795175827 + 1.6875 Combine like terms: -1.795175827 + 1.6875 = -0.107675827 x = -0.107675827 Simplifying x = -0.107675827Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.482675827, -0.107675827}
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