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Simplifying 4(4x + 1) = 3x + -4x(6 + -1x) + -8 Reorder the terms: 4(1 + 4x) = 3x + -4x(6 + -1x) + -8 (1 * 4 + 4x * 4) = 3x + -4x(6 + -1x) + -8 (4 + 16x) = 3x + -4x(6 + -1x) + -8 4 + 16x = 3x + (6 * -4x + -1x * -4x) + -8 4 + 16x = 3x + (-24x + 4x2) + -8 Reorder the terms: 4 + 16x = -8 + 3x + -24x + 4x2 Combine like terms: 3x + -24x = -21x 4 + 16x = -8 + -21x + 4x2 Solving 4 + 16x = -8 + -21x + 4x2 Solving for variable 'x'. Reorder the terms: 4 + 8 + 16x + 21x + -4x2 = -8 + -21x + 4x2 + 8 + 21x + -4x2 Combine like terms: 4 + 8 = 12 12 + 16x + 21x + -4x2 = -8 + -21x + 4x2 + 8 + 21x + -4x2 Combine like terms: 16x + 21x = 37x 12 + 37x + -4x2 = -8 + -21x + 4x2 + 8 + 21x + -4x2 Reorder the terms: 12 + 37x + -4x2 = -8 + 8 + -21x + 21x + 4x2 + -4x2 Combine like terms: -8 + 8 = 0 12 + 37x + -4x2 = 0 + -21x + 21x + 4x2 + -4x2 12 + 37x + -4x2 = -21x + 21x + 4x2 + -4x2 Combine like terms: -21x + 21x = 0 12 + 37x + -4x2 = 0 + 4x2 + -4x2 12 + 37x + -4x2 = 4x2 + -4x2 Combine like terms: 4x2 + -4x2 = 0 12 + 37x + -4x2 = 0 Begin completing the square. Divide all terms by -4 the coefficient of the squared term: Divide each side by '-4'. -3 + -9.25x + x2 = 0 Move the constant term to the right: Add '3' to each side of the equation. -3 + -9.25x + 3 + x2 = 0 + 3 Reorder the terms: -3 + 3 + -9.25x + x2 = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -9.25x + x2 = 0 + 3 -9.25x + x2 = 0 + 3 Combine like terms: 0 + 3 = 3 -9.25x + x2 = 3 The x term is -9.25x. Take half its coefficient (-4.625). Square it (21.390625) and add it to both sides. Add '21.390625' to each side of the equation. -9.25x + 21.390625 + x2 = 3 + 21.390625 Reorder the terms: 21.390625 + -9.25x + x2 = 3 + 21.390625 Combine like terms: 3 + 21.390625 = 24.390625 21.390625 + -9.25x + x2 = 24.390625 Factor a perfect square on the left side: (x + -4.625)(x + -4.625) = 24.390625 Calculate the square root of the right side: 4.938686566 Break this problem into two subproblems by setting (x + -4.625) equal to 4.938686566 and -4.938686566.Subproblem 1
x + -4.625 = 4.938686566 Simplifying x + -4.625 = 4.938686566 Reorder the terms: -4.625 + x = 4.938686566 Solving -4.625 + x = 4.938686566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = 4.938686566 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = 4.938686566 + 4.625 x = 4.938686566 + 4.625 Combine like terms: 4.938686566 + 4.625 = 9.563686566 x = 9.563686566 Simplifying x = 9.563686566Subproblem 2
x + -4.625 = -4.938686566 Simplifying x + -4.625 = -4.938686566 Reorder the terms: -4.625 + x = -4.938686566 Solving -4.625 + x = -4.938686566 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4.625' to each side of the equation. -4.625 + 4.625 + x = -4.938686566 + 4.625 Combine like terms: -4.625 + 4.625 = 0.000 0.000 + x = -4.938686566 + 4.625 x = -4.938686566 + 4.625 Combine like terms: -4.938686566 + 4.625 = -0.313686566 x = -0.313686566 Simplifying x = -0.313686566Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.563686566, -0.313686566}
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