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Simplifying 4x2 + -4x = 5x + 11 Reorder the terms: -4x + 4x2 = 5x + 11 Reorder the terms: -4x + 4x2 = 11 + 5x Solving -4x + 4x2 = 11 + 5x Solving for variable 'x'. Reorder the terms: -11 + -4x + -5x + 4x2 = 11 + 5x + -11 + -5x Combine like terms: -4x + -5x = -9x -11 + -9x + 4x2 = 11 + 5x + -11 + -5x Reorder the terms: -11 + -9x + 4x2 = 11 + -11 + 5x + -5x Combine like terms: 11 + -11 = 0 -11 + -9x + 4x2 = 0 + 5x + -5x -11 + -9x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -11 + -9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2.75 + -2.25x + x2 = 0 Move the constant term to the right: Add '2.75' to each side of the equation. -2.75 + -2.25x + 2.75 + x2 = 0 + 2.75 Reorder the terms: -2.75 + 2.75 + -2.25x + x2 = 0 + 2.75 Combine like terms: -2.75 + 2.75 = 0.00 0.00 + -2.25x + x2 = 0 + 2.75 -2.25x + x2 = 0 + 2.75 Combine like terms: 0 + 2.75 = 2.75 -2.25x + x2 = 2.75 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 = 2.75 + 1.265625 Reorder the terms: 1.265625 + -2.25x + x2 = 2.75 + 1.265625 Combine like terms: 2.75 + 1.265625 = 4.015625 1.265625 + -2.25x + x2 = 4.015625 Factor a perfect square on the left side: (x + -1.125)(x + -1.125) = 4.015625 Calculate the square root of the right side: 2.003902443 Break this problem into two subproblems by setting (x + -1.125) equal to 2.003902443 and -2.003902443.Subproblem 1
x + -1.125 = 2.003902443 Simplifying x + -1.125 = 2.003902443 Reorder the terms: -1.125 + x = 2.003902443 Solving -1.125 + x = 2.003902443 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 = 2.003902443 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = 2.003902443 + 1.125 x = 2.003902443 + 1.125 Combine like terms: 2.003902443 + 1.125 = 3.128902443 x = 3.128902443 Simplifying x = 3.128902443Subproblem 2
x + -1.125 = -2.003902443 Simplifying x + -1.125 = -2.003902443 Reorder the terms: -1.125 + x = -2.003902443 Solving -1.125 + x = -2.003902443 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 = -2.003902443 + 1.125 Combine like terms: -1.125 + 1.125 = 0.000 0.000 + x = -2.003902443 + 1.125 x = -2.003902443 + 1.125 Combine like terms: -2.003902443 + 1.125 = -0.878902443 x = -0.878902443 Simplifying x = -0.878902443Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.128902443, -0.878902443}
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