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Simplifying 4x(x + -4) = 33 + -3x Reorder the terms: 4x(-4 + x) = 33 + -3x (-4 * 4x + x * 4x) = 33 + -3x (-16x + 4x2) = 33 + -3x Solving -16x + 4x2 = 33 + -3x Solving for variable 'x'. Reorder the terms: -33 + -16x + 3x + 4x2 = 33 + -3x + -33 + 3x Combine like terms: -16x + 3x = -13x -33 + -13x + 4x2 = 33 + -3x + -33 + 3x Reorder the terms: -33 + -13x + 4x2 = 33 + -33 + -3x + 3x Combine like terms: 33 + -33 = 0 -33 + -13x + 4x2 = 0 + -3x + 3x -33 + -13x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -33 + -13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -8.25 + -3.25x + x2 = 0 Move the constant term to the right: Add '8.25' to each side of the equation. -8.25 + -3.25x + 8.25 + x2 = 0 + 8.25 Reorder the terms: -8.25 + 8.25 + -3.25x + x2 = 0 + 8.25 Combine like terms: -8.25 + 8.25 = 0.00 0.00 + -3.25x + x2 = 0 + 8.25 -3.25x + x2 = 0 + 8.25 Combine like terms: 0 + 8.25 = 8.25 -3.25x + x2 = 8.25 The x term is -3.25x. Take half its coefficient (-1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. -3.25x + 2.640625 + x2 = 8.25 + 2.640625 Reorder the terms: 2.640625 + -3.25x + x2 = 8.25 + 2.640625 Combine like terms: 8.25 + 2.640625 = 10.890625 2.640625 + -3.25x + x2 = 10.890625 Factor a perfect square on the left side: (x + -1.625)(x + -1.625) = 10.890625 Calculate the square root of the right side: 3.300094696 Break this problem into two subproblems by setting (x + -1.625) equal to 3.300094696 and -3.300094696.Subproblem 1
x + -1.625 = 3.300094696 Simplifying x + -1.625 = 3.300094696 Reorder the terms: -1.625 + x = 3.300094696 Solving -1.625 + x = 3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = 3.300094696 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = 3.300094696 + 1.625 x = 3.300094696 + 1.625 Combine like terms: 3.300094696 + 1.625 = 4.925094696 x = 4.925094696 Simplifying x = 4.925094696Subproblem 2
x + -1.625 = -3.300094696 Simplifying x + -1.625 = -3.300094696 Reorder the terms: -1.625 + x = -3.300094696 Solving -1.625 + x = -3.300094696 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.625' to each side of the equation. -1.625 + 1.625 + x = -3.300094696 + 1.625 Combine like terms: -1.625 + 1.625 = 0.000 0.000 + x = -3.300094696 + 1.625 x = -3.300094696 + 1.625 Combine like terms: -3.300094696 + 1.625 = -1.675094696 x = -1.675094696 Simplifying x = -1.675094696Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.925094696, -1.675094696}
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