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Simplifying (4x2 + -1x + -3) + (4x2 + -4x + -1) = 0 Reorder the terms: (-3 + -1x + 4x2) + (4x2 + -4x + -1) = 0 Remove parenthesis around (-3 + -1x + 4x2) -3 + -1x + 4x2 + (4x2 + -4x + -1) = 0 Reorder the terms: -3 + -1x + 4x2 + (-1 + -4x + 4x2) = 0 Remove parenthesis around (-1 + -4x + 4x2) -3 + -1x + 4x2 + -1 + -4x + 4x2 = 0 Reorder the terms: -3 + -1 + -1x + -4x + 4x2 + 4x2 = 0 Combine like terms: -3 + -1 = -4 -4 + -1x + -4x + 4x2 + 4x2 = 0 Combine like terms: -1x + -4x = -5x -4 + -5x + 4x2 + 4x2 = 0 Combine like terms: 4x2 + 4x2 = 8x2 -4 + -5x + 8x2 = 0 Solving -4 + -5x + 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'. -0.5 + -0.625x + x2 = 0 Move the constant term to the right: Add '0.5' to each side of the equation. -0.5 + -0.625x + 0.5 + x2 = 0 + 0.5 Reorder the terms: -0.5 + 0.5 + -0.625x + x2 = 0 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + -0.625x + x2 = 0 + 0.5 -0.625x + x2 = 0 + 0.5 Combine like terms: 0 + 0.5 = 0.5 -0.625x + x2 = 0.5 The x term is -0.625x. Take half its coefficient (-0.3125). Square it (0.09765625) and add it to both sides. Add '0.09765625' to each side of the equation. -0.625x + 0.09765625 + x2 = 0.5 + 0.09765625 Reorder the terms: 0.09765625 + -0.625x + x2 = 0.5 + 0.09765625 Combine like terms: 0.5 + 0.09765625 = 0.59765625 0.09765625 + -0.625x + x2 = 0.59765625 Factor a perfect square on the left side: (x + -0.3125)(x + -0.3125) = 0.59765625 Calculate the square root of the right side: 0.773082305 Break this problem into two subproblems by setting (x + -0.3125) equal to 0.773082305 and -0.773082305.Subproblem 1
x + -0.3125 = 0.773082305 Simplifying x + -0.3125 = 0.773082305 Reorder the terms: -0.3125 + x = 0.773082305 Solving -0.3125 + x = 0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = 0.773082305 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = 0.773082305 + 0.3125 x = 0.773082305 + 0.3125 Combine like terms: 0.773082305 + 0.3125 = 1.085582305 x = 1.085582305 Simplifying x = 1.085582305Subproblem 2
x + -0.3125 = -0.773082305 Simplifying x + -0.3125 = -0.773082305 Reorder the terms: -0.3125 + x = -0.773082305 Solving -0.3125 + x = -0.773082305 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3125' to each side of the equation. -0.3125 + 0.3125 + x = -0.773082305 + 0.3125 Combine like terms: -0.3125 + 0.3125 = 0.0000 0.0000 + x = -0.773082305 + 0.3125 x = -0.773082305 + 0.3125 Combine like terms: -0.773082305 + 0.3125 = -0.460582305 x = -0.460582305 Simplifying x = -0.460582305Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.085582305, -0.460582305}
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