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Simplifying 4x(x + -2) + -3x(x + 1) = 18 Reorder the terms: 4x(-2 + x) + -3x(x + 1) = 18 (-2 * 4x + x * 4x) + -3x(x + 1) = 18 (-8x + 4x2) + -3x(x + 1) = 18 Reorder the terms: -8x + 4x2 + -3x(1 + x) = 18 -8x + 4x2 + (1 * -3x + x * -3x) = 18 -8x + 4x2 + (-3x + -3x2) = 18 Reorder the terms: -8x + -3x + 4x2 + -3x2 = 18 Combine like terms: -8x + -3x = -11x -11x + 4x2 + -3x2 = 18 Combine like terms: 4x2 + -3x2 = 1x2 -11x + 1x2 = 18 Solving -11x + 1x2 = 18 Solving for variable 'x'. Reorder the terms: -18 + -11x + 1x2 = 18 + -18 Combine like terms: 18 + -18 = 0 -18 + -11x + 1x2 = 0 Begin completing the square. Move the constant term to the right: Add '18' to each side of the equation. -18 + -11x + 18 + x2 = 0 + 18 Reorder the terms: -18 + 18 + -11x + x2 = 0 + 18 Combine like terms: -18 + 18 = 0 0 + -11x + x2 = 0 + 18 -11x + x2 = 0 + 18 Combine like terms: 0 + 18 = 18 -11x + x2 = 18 The x term is -11x. Take half its coefficient (-5.5). Square it (30.25) and add it to both sides. Add '30.25' to each side of the equation. -11x + 30.25 + x2 = 18 + 30.25 Reorder the terms: 30.25 + -11x + x2 = 18 + 30.25 Combine like terms: 18 + 30.25 = 48.25 30.25 + -11x + x2 = 48.25 Factor a perfect square on the left side: (x + -5.5)(x + -5.5) = 48.25 Calculate the square root of the right side: 6.946221995 Break this problem into two subproblems by setting (x + -5.5) equal to 6.946221995 and -6.946221995.Subproblem 1
x + -5.5 = 6.946221995 Simplifying x + -5.5 = 6.946221995 Reorder the terms: -5.5 + x = 6.946221995 Solving -5.5 + x = 6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = 6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = 6.946221995 + 5.5 x = 6.946221995 + 5.5 Combine like terms: 6.946221995 + 5.5 = 12.446221995 x = 12.446221995 Simplifying x = 12.446221995Subproblem 2
x + -5.5 = -6.946221995 Simplifying x + -5.5 = -6.946221995 Reorder the terms: -5.5 + x = -6.946221995 Solving -5.5 + x = -6.946221995 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.5' to each side of the equation. -5.5 + 5.5 + x = -6.946221995 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + x = -6.946221995 + 5.5 x = -6.946221995 + 5.5 Combine like terms: -6.946221995 + 5.5 = -1.446221995 x = -1.446221995 Simplifying x = -1.446221995Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.446221995, -1.446221995}
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