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Simplifying 4x(-2x + 3) = 8x + -33 Reorder the terms: 4x(3 + -2x) = 8x + -33 (3 * 4x + -2x * 4x) = 8x + -33 (12x + -8x2) = 8x + -33 Reorder the terms: 12x + -8x2 = -33 + 8x Solving 12x + -8x2 = -33 + 8x Solving for variable 'x'. Reorder the terms: 33 + 12x + -8x + -8x2 = -33 + 8x + 33 + -8x Combine like terms: 12x + -8x = 4x 33 + 4x + -8x2 = -33 + 8x + 33 + -8x Reorder the terms: 33 + 4x + -8x2 = -33 + 33 + 8x + -8x Combine like terms: -33 + 33 = 0 33 + 4x + -8x2 = 0 + 8x + -8x 33 + 4x + -8x2 = 8x + -8x Combine like terms: 8x + -8x = 0 33 + 4x + -8x2 = 0 Begin completing the square. Divide all terms by -8 the coefficient of the squared term: Divide each side by '-8'. -4.125 + -0.5x + x2 = 0 Move the constant term to the right: Add '4.125' to each side of the equation. -4.125 + -0.5x + 4.125 + x2 = 0 + 4.125 Reorder the terms: -4.125 + 4.125 + -0.5x + x2 = 0 + 4.125 Combine like terms: -4.125 + 4.125 = 0.000 0.000 + -0.5x + x2 = 0 + 4.125 -0.5x + x2 = 0 + 4.125 Combine like terms: 0 + 4.125 = 4.125 -0.5x + x2 = 4.125 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 4.125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 4.125 + 0.0625 Combine like terms: 4.125 + 0.0625 = 4.1875 0.0625 + -0.5x + x2 = 4.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 4.1875 Calculate the square root of the right side: 2.046338193 Break this problem into two subproblems by setting (x + -0.25) equal to 2.046338193 and -2.046338193.Subproblem 1
x + -0.25 = 2.046338193 Simplifying x + -0.25 = 2.046338193 Reorder the terms: -0.25 + x = 2.046338193 Solving -0.25 + x = 2.046338193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 2.046338193 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 2.046338193 + 0.25 x = 2.046338193 + 0.25 Combine like terms: 2.046338193 + 0.25 = 2.296338193 x = 2.296338193 Simplifying x = 2.296338193Subproblem 2
x + -0.25 = -2.046338193 Simplifying x + -0.25 = -2.046338193 Reorder the terms: -0.25 + x = -2.046338193 Solving -0.25 + x = -2.046338193 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -2.046338193 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -2.046338193 + 0.25 x = -2.046338193 + 0.25 Combine like terms: -2.046338193 + 0.25 = -1.796338193 x = -1.796338193 Simplifying x = -1.796338193Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.296338193, -1.796338193}
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