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Simplifying 3x + -4(4x + 5) = -1x(x + 4) + -3x2 + -5 Reorder the terms: 3x + -4(5 + 4x) = -1x(x + 4) + -3x2 + -5 3x + (5 * -4 + 4x * -4) = -1x(x + 4) + -3x2 + -5 3x + (-20 + -16x) = -1x(x + 4) + -3x2 + -5 Reorder the terms: -20 + 3x + -16x = -1x(x + 4) + -3x2 + -5 Combine like terms: 3x + -16x = -13x -20 + -13x = -1x(x + 4) + -3x2 + -5 Reorder the terms: -20 + -13x = -1x(4 + x) + -3x2 + -5 -20 + -13x = (4 * -1x + x * -1x) + -3x2 + -5 -20 + -13x = (-4x + -1x2) + -3x2 + -5 Reorder the terms: -20 + -13x = -5 + -4x + -1x2 + -3x2 Combine like terms: -1x2 + -3x2 = -4x2 -20 + -13x = -5 + -4x + -4x2 Solving -20 + -13x = -5 + -4x + -4x2 Solving for variable 'x'. Reorder the terms: -20 + 5 + -13x + 4x + 4x2 = -5 + -4x + -4x2 + 5 + 4x + 4x2 Combine like terms: -20 + 5 = -15 -15 + -13x + 4x + 4x2 = -5 + -4x + -4x2 + 5 + 4x + 4x2 Combine like terms: -13x + 4x = -9x -15 + -9x + 4x2 = -5 + -4x + -4x2 + 5 + 4x + 4x2 Reorder the terms: -15 + -9x + 4x2 = -5 + 5 + -4x + 4x + -4x2 + 4x2 Combine like terms: -5 + 5 = 0 -15 + -9x + 4x2 = 0 + -4x + 4x + -4x2 + 4x2 -15 + -9x + 4x2 = -4x + 4x + -4x2 + 4x2 Combine like terms: -4x + 4x = 0 -15 + -9x + 4x2 = 0 + -4x2 + 4x2 -15 + -9x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -15 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -3.75 + -2.25x + x2 = 0 Move the constant term to the right: Add '3.75' to each side of the equation. -3.75 + -2.25x + 3.75 + x2 = 0 + 3.75 Reorder the terms: -3.75 + 3.75 + -2.25x + x2 = 0 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + -2.25x + x2 = 0 + 3.75 -2.25x + x2 = 0 + 3.75 Combine like terms: 0 + 3.75 = 3.75 -2.25x + x2 = 3.75 The x term is -2.25x. Take half its coefficient (-1.125). Square it (1.265625) and add it to both sides. Add '1.265625' to each side of the equation. -2.25x + 1.265625 + x2 = 3.75 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 3.75 + 1.265625 Combine like terms: 3.75 + 1.265625 = 5.015625 1.265625 + -2.25x + x2 = 5.015625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (x + -1.125) equal to 2.239559108 and -2.239559108.Subproblem 1
x + -1.125 = 2.239559108 Simplifying x + -1.125 = 2.239559108 Reorder the terms: -1.125 + x = 2.239559108 Solving -1.125 + x = 2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = 2.239559108 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.239559108 + 1.125 x = 2.239559108 + 1.125 Combine like terms: 2.239559108 + 1.125 = 3.364559108 x = 3.364559108 Simplifying x = 3.364559108Subproblem 2
x + -1.125 = -2.239559108 Simplifying x + -1.125 = -2.239559108 Reorder the terms: -1.125 + x = -2.239559108 Solving -1.125 + x = -2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.125' to each side of the equation. -1.125 + 1.125 + x = -2.239559108 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.239559108 + 1.125 x = -2.239559108 + 1.125 Combine like terms: -2.239559108 + 1.125 = -1.114559108 x = -1.114559108 Simplifying x = -1.114559108Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.364559108, -1.114559108}
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