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Simplifying 4x(x + 6) + -2x = 5x + 2 Reorder the terms: 4x(6 + x) + -2x = 5x + 2 (6 * 4x + x * 4x) + -2x = 5x + 2 (24x + 4x2) + -2x = 5x + 2 Reorder the terms: 24x + -2x + 4x2 = 5x + 2 Combine like terms: 24x + -2x = 22x 22x + 4x2 = 5x + 2 Reorder the terms: 22x + 4x2 = 2 + 5x Solving 22x + 4x2 = 2 + 5x Solving for variable 'x'. Reorder the terms: -2 + 22x + -5x + 4x2 = 2 + 5x + -2 + -5x Combine like terms: 22x + -5x = 17x -2 + 17x + 4x2 = 2 + 5x + -2 + -5x Reorder the terms: -2 + 17x + 4x2 = 2 + -2 + 5x + -5x Combine like terms: 2 + -2 = 0 -2 + 17x + 4x2 = 0 + 5x + -5x -2 + 17x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -2 + 17x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.5 + 4.25x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + 4.25x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + 4.25x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + 4.25x + x2 = 0 + 0.5 4.25x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 4.25x + x2 = 0.5 The x term is 4.25x. Take half its coefficient (2.125). Square it (4.515625) and add it to both sides. Add '4.515625' to each side of the equation. 4.25x + 4.515625 + x2 = 0.5 + 4.515625 Reorder the terms: 4.515625 + 4.25x + x2 = 0.5 + 4.515625 Combine like terms: 0.5 + 4.515625 = 5.015625 4.515625 + 4.25x + x2 = 5.015625 Factor a perfect square on the left side: (x + 2.125)(x + 2.125) = 5.015625 Calculate the square root of the right side: 2.239559108 Break this problem into two subproblems by setting (x + 2.125) equal to 2.239559108 and -2.239559108.Subproblem 1
x + 2.125 = 2.239559108 Simplifying x + 2.125 = 2.239559108 Reorder the terms: 2.125 + x = 2.239559108 Solving 2.125 + x = 2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = 2.239559108 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = 2.239559108 + -2.125 x = 2.239559108 + -2.125 Combine like terms: 2.239559108 + -2.125 = 0.114559108 x = 0.114559108 Simplifying x = 0.114559108Subproblem 2
x + 2.125 = -2.239559108 Simplifying x + 2.125 = -2.239559108 Reorder the terms: 2.125 + x = -2.239559108 Solving 2.125 + x = -2.239559108 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.125' to each side of the equation. 2.125 + -2.125 + x = -2.239559108 + -2.125 Combine like terms: 2.125 + -2.125 = 0.000 0.000 + x = -2.239559108 + -2.125 x = -2.239559108 + -2.125 Combine like terms: -2.239559108 + -2.125 = -4.364559108 x = -4.364559108 Simplifying x = -4.364559108Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.114559108, -4.364559108}
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