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Simplifying 16x2 + -8x + -3 + -5x2 + -2x + 1 = 0 Reorder the terms: -3 + 1 + -8x + -2x + 16x2 + -5x2 = 0 Combine like terms: -3 + 1 = -2 -2 + -8x + -2x + 16x2 + -5x2 = 0 Combine like terms: -8x + -2x = -10x -2 + -10x + 16x2 + -5x2 = 0 Combine like terms: 16x2 + -5x2 = 11x2 -2 + -10x + 11x2 = 0 Solving -2 + -10x + 11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. -0.1818181818 + -0.9090909091x + x2 = 0 Move the constant term to the right: Add '0.1818181818' to each side of the equation. -0.1818181818 + -0.9090909091x + 0.1818181818 + x2 = 0 + 0.1818181818 Reorder the terms: -0.1818181818 + 0.1818181818 + -0.9090909091x + x2 = 0 + 0.1818181818 Combine like terms: -0.1818181818 + 0.1818181818 = 0.0000000000 0.0000000000 + -0.9090909091x + x2 = 0 + 0.1818181818 -0.9090909091x + x2 = 0 + 0.1818181818 Combine like terms: 0 + 0.1818181818 = 0.1818181818 -0.9090909091x + x2 = 0.1818181818 The x term is -0.9090909091x. Take half its coefficient (-0.4545454546). Square it (0.2066115703) and add it to both sides. Add '0.2066115703' to each side of the equation. -0.9090909091x + 0.2066115703 + x2 = 0.1818181818 + 0.2066115703 Reorder the terms: 0.2066115703 + -0.9090909091x + x2 = 0.1818181818 + 0.2066115703 Combine like terms: 0.1818181818 + 0.2066115703 = 0.3884297521 0.2066115703 + -0.9090909091x + x2 = 0.3884297521 Factor a perfect square on the left side: (x + -0.4545454546)(x + -0.4545454546) = 0.3884297521 Calculate the square root of the right side: 0.623241327 Break this problem into two subproblems by setting (x + -0.4545454546) equal to 0.623241327 and -0.623241327.Subproblem 1
x + -0.4545454546 = 0.623241327 Simplifying x + -0.4545454546 = 0.623241327 Reorder the terms: -0.4545454546 + x = 0.623241327 Solving -0.4545454546 + x = 0.623241327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = 0.623241327 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = 0.623241327 + 0.4545454546 x = 0.623241327 + 0.4545454546 Combine like terms: 0.623241327 + 0.4545454546 = 1.0777867816 x = 1.0777867816 Simplifying x = 1.0777867816Subproblem 2
x + -0.4545454546 = -0.623241327 Simplifying x + -0.4545454546 = -0.623241327 Reorder the terms: -0.4545454546 + x = -0.623241327 Solving -0.4545454546 + x = -0.623241327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4545454546' to each side of the equation. -0.4545454546 + 0.4545454546 + x = -0.623241327 + 0.4545454546 Combine like terms: -0.4545454546 + 0.4545454546 = 0.0000000000 0.0000000000 + x = -0.623241327 + 0.4545454546 x = -0.623241327 + 0.4545454546 Combine like terms: -0.623241327 + 0.4545454546 = -0.1686958724 x = -0.1686958724 Simplifying x = -0.1686958724Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.0777867816, -0.1686958724}
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