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Simplifying 3 + -4(x + -2) = 8x(2x + -1) Reorder the terms: 3 + -4(-2 + x) = 8x(2x + -1) 3 + (-2 * -4 + x * -4) = 8x(2x + -1) 3 + (8 + -4x) = 8x(2x + -1) Combine like terms: 3 + 8 = 11 11 + -4x = 8x(2x + -1) Reorder the terms: 11 + -4x = 8x(-1 + 2x) 11 + -4x = (-1 * 8x + 2x * 8x) 11 + -4x = (-8x + 16x2) Solving 11 + -4x = -8x + 16x2 Solving for variable 'x'. Combine like terms: -4x + 8x = 4x 11 + 4x + -16x2 = -8x + 16x2 + 8x + -16x2 Reorder the terms: 11 + 4x + -16x2 = -8x + 8x + 16x2 + -16x2 Combine like terms: -8x + 8x = 0 11 + 4x + -16x2 = 0 + 16x2 + -16x2 11 + 4x + -16x2 = 16x2 + -16x2 Combine like terms: 16x2 + -16x2 = 0 11 + 4x + -16x2 = 0 Begin completing the square. Divide all terms by -16 the coefficient of the squared term: Divide each side by '-16'. -0.6875 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.6875' to each side of the equation. -0.6875 + -0.25x + 0.6875 + x2 = 0 + 0.6875 Reorder the terms: -0.6875 + 0.6875 + -0.25x + x2 = 0 + 0.6875 Combine like terms: -0.6875 + 0.6875 = 0.0000 0.0000 + -0.25x + x2 = 0 + 0.6875 -0.25x + x2 = 0 + 0.6875 Combine like terms: 0 + 0.6875 = 0.6875 -0.25x + x2 = 0.6875 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.6875 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.6875 + 0.015625 Combine like terms: 0.6875 + 0.015625 = 0.703125 0.015625 + -0.25x + x2 = 0.703125 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.703125 Calculate the square root of the right side: 0.838525492 Break this problem into two subproblems by setting (x + -0.125) equal to 0.838525492 and -0.838525492.Subproblem 1
x + -0.125 = 0.838525492 Simplifying x + -0.125 = 0.838525492 Reorder the terms: -0.125 + x = 0.838525492 Solving -0.125 + x = 0.838525492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.838525492 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.838525492 + 0.125 x = 0.838525492 + 0.125 Combine like terms: 0.838525492 + 0.125 = 0.963525492 x = 0.963525492 Simplifying x = 0.963525492Subproblem 2
x + -0.125 = -0.838525492 Simplifying x + -0.125 = -0.838525492 Reorder the terms: -0.125 + x = -0.838525492 Solving -0.125 + x = -0.838525492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.838525492 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.838525492 + 0.125 x = -0.838525492 + 0.125 Combine like terms: -0.838525492 + 0.125 = -0.713525492 x = -0.713525492 Simplifying x = -0.713525492Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.963525492, -0.713525492}
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