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Simplifying 31x(x + -1) = 6 Reorder the terms: 31x(-1 + x) = 6 (-1 * 31x + x * 31x) = 6 (-31x + 31x2) = 6 Solving -31x + 31x2 = 6 Solving for variable 'x'. Reorder the terms: -6 + -31x + 31x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -6 + -31x + 31x2 = 0 Begin completing the square. Divide all terms by 31 the coefficient of the squared term: Divide each side by '31'. -0.1935483871 + -1x + x2 = 0 Move the constant term to the right: Add '0.1935483871' to each side of the equation. -0.1935483871 + -1x + 0.1935483871 + x2 = 0 + 0.1935483871 Reorder the terms: -0.1935483871 + 0.1935483871 + -1x + x2 = 0 + 0.1935483871 Combine like terms: -0.1935483871 + 0.1935483871 = 0.0000000000 0.0000000000 + -1x + x2 = 0 + 0.1935483871 -1x + x2 = 0 + 0.1935483871 Combine like terms: 0 + 0.1935483871 = 0.1935483871 -1x + x2 = 0.1935483871 The x term is -1x. Take half its coefficient (-0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. -1x + 0.25 + x2 = 0.1935483871 + 0.25 Reorder the terms: 0.25 + -1x + x2 = 0.1935483871 + 0.25 Combine like terms: 0.1935483871 + 0.25 = 0.4435483871 0.25 + -1x + x2 = 0.4435483871 Factor a perfect square on the left side: (x + -0.5)(x + -0.5) = 0.4435483871 Calculate the square root of the right side: 0.665994285 Break this problem into two subproblems by setting (x + -0.5) equal to 0.665994285 and -0.665994285.Subproblem 1
x + -0.5 = 0.665994285 Simplifying x + -0.5 = 0.665994285 Reorder the terms: -0.5 + x = 0.665994285 Solving -0.5 + x = 0.665994285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = 0.665994285 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = 0.665994285 + 0.5 x = 0.665994285 + 0.5 Combine like terms: 0.665994285 + 0.5 = 1.165994285 x = 1.165994285 Simplifying x = 1.165994285Subproblem 2
x + -0.5 = -0.665994285 Simplifying x + -0.5 = -0.665994285 Reorder the terms: -0.5 + x = -0.665994285 Solving -0.5 + x = -0.665994285 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.5' to each side of the equation. -0.5 + 0.5 + x = -0.665994285 + 0.5 Combine like terms: -0.5 + 0.5 = 0.0 0.0 + x = -0.665994285 + 0.5 x = -0.665994285 + 0.5 Combine like terms: -0.665994285 + 0.5 = -0.165994285 x = -0.165994285 Simplifying x = -0.165994285Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.165994285, -0.165994285}
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