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Simplifying 2(4x + 2)(x + -1) + 3 = 0 Reorder the terms: 2(2 + 4x)(x + -1) + 3 = 0 Reorder the terms: 2(2 + 4x)(-1 + x) + 3 = 0 Multiply (2 + 4x) * (-1 + x) 2(2(-1 + x) + 4x * (-1 + x)) + 3 = 0 2((-1 * 2 + x * 2) + 4x * (-1 + x)) + 3 = 0 2((-2 + 2x) + 4x * (-1 + x)) + 3 = 0 2(-2 + 2x + (-1 * 4x + x * 4x)) + 3 = 0 2(-2 + 2x + (-4x + 4x2)) + 3 = 0 Combine like terms: 2x + -4x = -2x 2(-2 + -2x + 4x2) + 3 = 0 (-2 * 2 + -2x * 2 + 4x2 * 2) + 3 = 0 (-4 + -4x + 8x2) + 3 = 0 Reorder the terms: -4 + 3 + -4x + 8x2 = 0 Combine like terms: -4 + 3 = -1 -1 + -4x + 8x2 = 0 Solving -1 + -4x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. -0.125 + -0.5x + x2 = 0 Move the constant term to the right: Add '0.125' to each side of the equation. -0.125 + -0.5x + 0.125 + x2 = 0 + 0.125 Reorder the terms: -0.125 + 0.125 + -0.5x + x2 = 0 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + -0.5x + x2 = 0 + 0.125 -0.5x + x2 = 0 + 0.125 Combine like terms: 0 + 0.125 = 0.125 -0.5x + x2 = 0.125 The x term is -0.5x. Take half its coefficient (-0.25). Square it (0.0625) and add it to both sides. Add '0.0625' to each side of the equation. -0.5x + 0.0625 + x2 = 0.125 + 0.0625 Reorder the terms: 0.0625 + -0.5x + x2 = 0.125 + 0.0625 Combine like terms: 0.125 + 0.0625 = 0.1875 0.0625 + -0.5x + x2 = 0.1875 Factor a perfect square on the left side: (x + -0.25)(x + -0.25) = 0.1875 Calculate the square root of the right side: 0.433012702 Break this problem into two subproblems by setting (x + -0.25) equal to 0.433012702 and -0.433012702.Subproblem 1
x + -0.25 = 0.433012702 Simplifying x + -0.25 = 0.433012702 Reorder the terms: -0.25 + x = 0.433012702 Solving -0.25 + x = 0.433012702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = 0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = 0.433012702 + 0.25 x = 0.433012702 + 0.25 Combine like terms: 0.433012702 + 0.25 = 0.683012702 x = 0.683012702 Simplifying x = 0.683012702Subproblem 2
x + -0.25 = -0.433012702 Simplifying x + -0.25 = -0.433012702 Reorder the terms: -0.25 + x = -0.433012702 Solving -0.25 + x = -0.433012702 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.25' to each side of the equation. -0.25 + 0.25 + x = -0.433012702 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + x = -0.433012702 + 0.25 x = -0.433012702 + 0.25 Combine like terms: -0.433012702 + 0.25 = -0.183012702 x = -0.183012702 Simplifying x = -0.183012702Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.683012702, -0.183012702}
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