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Simplifying 3x + (-4)(x + 2) = 14 + -4x(x + 2) Reorder the terms: 3x + -4(2 + x) = 14 + -4x(x + 2) 3x + (2 * -4 + x * -4) = 14 + -4x(x + 2) 3x + (-8 + -4x) = 14 + -4x(x + 2) Reorder the terms: -8 + 3x + -4x = 14 + -4x(x + 2) Combine like terms: 3x + -4x = -1x -8 + -1x = 14 + -4x(x + 2) Reorder the terms: -8 + -1x = 14 + -4x(2 + x) -8 + -1x = 14 + (2 * -4x + x * -4x) -8 + -1x = 14 + (-8x + -4x2) Solving -8 + -1x = 14 + -8x + -4x2 Solving for variable 'x'. Reorder the terms: -8 + -14 + -1x + 8x + 4x2 = 14 + -8x + -4x2 + -14 + 8x + 4x2 Combine like terms: -8 + -14 = -22 -22 + -1x + 8x + 4x2 = 14 + -8x + -4x2 + -14 + 8x + 4x2 Combine like terms: -1x + 8x = 7x -22 + 7x + 4x2 = 14 + -8x + -4x2 + -14 + 8x + 4x2 Reorder the terms: -22 + 7x + 4x2 = 14 + -14 + -8x + 8x + -4x2 + 4x2 Combine like terms: 14 + -14 = 0 -22 + 7x + 4x2 = 0 + -8x + 8x + -4x2 + 4x2 -22 + 7x + 4x2 = -8x + 8x + -4x2 + 4x2 Combine like terms: -8x + 8x = 0 -22 + 7x + 4x2 = 0 + -4x2 + 4x2 -22 + 7x + 4x2 = -4x2 + 4x2 Combine like terms: -4x2 + 4x2 = 0 -22 + 7x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.5 + 1.75x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 1.75x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 1.75x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 1.75x + x2 = 0 + 5.5 1.75x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 1.75x + x2 = 5.5 The x term is 1.75x. Take half its coefficient (0.875). Square it (0.765625) and add it to both sides. Add '0.765625' to each side of the equation. 1.75x + 0.765625 + x2 = 5.5 + 0.765625 Reorder the terms: 0.765625 + 1.75x + x2 = 5.5 + 0.765625 Combine like terms: 5.5 + 0.765625 = 6.265625 0.765625 + 1.75x + x2 = 6.265625 Factor a perfect square on the left side: (x + 0.875)(x + 0.875) = 6.265625 Calculate the square root of the right side: 2.503123049 Break this problem into two subproblems by setting (x + 0.875) equal to 2.503123049 and -2.503123049.Subproblem 1
x + 0.875 = 2.503123049 Simplifying x + 0.875 = 2.503123049 Reorder the terms: 0.875 + x = 2.503123049 Solving 0.875 + x = 2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = 2.503123049 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = 2.503123049 + -0.875 x = 2.503123049 + -0.875 Combine like terms: 2.503123049 + -0.875 = 1.628123049 x = 1.628123049 Simplifying x = 1.628123049Subproblem 2
x + 0.875 = -2.503123049 Simplifying x + 0.875 = -2.503123049 Reorder the terms: 0.875 + x = -2.503123049 Solving 0.875 + x = -2.503123049 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.875' to each side of the equation. 0.875 + -0.875 + x = -2.503123049 + -0.875 Combine like terms: 0.875 + -0.875 = 0.000 0.000 + x = -2.503123049 + -0.875 x = -2.503123049 + -0.875 Combine like terms: -2.503123049 + -0.875 = -3.378123049 x = -3.378123049 Simplifying x = -3.378123049Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.628123049, -3.378123049}
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