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Simplifying 4x(x + 1) + 2x = 8 + -3x Reorder the terms: 4x(1 + x) + 2x = 8 + -3x (1 * 4x + x * 4x) + 2x = 8 + -3x (4x + 4x2) + 2x = 8 + -3x Reorder the terms: 4x + 2x + 4x2 = 8 + -3x Combine like terms: 4x + 2x = 6x 6x + 4x2 = 8 + -3x Solving 6x + 4x2 = 8 + -3x Solving for variable 'x'. Reorder the terms: -8 + 6x + 3x + 4x2 = 8 + -3x + -8 + 3x Combine like terms: 6x + 3x = 9x -8 + 9x + 4x2 = 8 + -3x + -8 + 3x Reorder the terms: -8 + 9x + 4x2 = 8 + -8 + -3x + 3x Combine like terms: 8 + -8 = 0 -8 + 9x + 4x2 = 0 + -3x + 3x -8 + 9x + 4x2 = -3x + 3x Combine like terms: -3x + 3x = 0 -8 + 9x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 2.25x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 2.25x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 2.25x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 2.25x + x2 = 0 + 2 2.25x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 2.25x + x2 = 2 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 + 1.265625 Reorder the terms: 1.265625 + 2.25x + x2 = 2 + 1.265625 Combine like terms: 2 + 1.265625 = 3.265625 1.265625 + 2.25x + x2 = 3.265625 Factor a perfect square on the left side: (x + 1.125)(x + 1.125) = 3.265625 Calculate the square root of the right side: 1.807104037 Break this problem into two subproblems by setting (x + 1.125) equal to 1.807104037 and -1.807104037.Subproblem 1
x + 1.125 = 1.807104037 Simplifying x + 1.125 = 1.807104037 Reorder the terms: 1.125 + x = 1.807104037 Solving 1.125 + x = 1.807104037 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 = 1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = 1.807104037 + -1.125 x = 1.807104037 + -1.125 Combine like terms: 1.807104037 + -1.125 = 0.682104037 x = 0.682104037 Simplifying x = 0.682104037Subproblem 2
x + 1.125 = -1.807104037 Simplifying x + 1.125 = -1.807104037 Reorder the terms: 1.125 + x = -1.807104037 Solving 1.125 + x = -1.807104037 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 = -1.807104037 + -1.125 Combine like terms: 1.125 + -1.125 = 0.000 0.000 + x = -1.807104037 + -1.125 x = -1.807104037 + -1.125 Combine like terms: -1.807104037 + -1.125 = -2.932104037 x = -2.932104037 Simplifying x = -2.932104037Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.682104037, -2.932104037}
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