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Simplifying x(1 + -1x) + 2x + -4 = 8x + -24x2 (1 * x + -1x * x) + 2x + -4 = 8x + -24x2 (1x + -1x2) + 2x + -4 = 8x + -24x2 Reorder the terms: -4 + 1x + 2x + -1x2 = 8x + -24x2 Combine like terms: 1x + 2x = 3x -4 + 3x + -1x2 = 8x + -24x2 Solving -4 + 3x + -1x2 = 8x + -24x2 Solving for variable 'x'. Reorder the terms: -4 + 3x + -8x + -1x2 + 24x2 = 8x + -24x2 + -8x + 24x2 Combine like terms: 3x + -8x = -5x -4 + -5x + -1x2 + 24x2 = 8x + -24x2 + -8x + 24x2 Combine like terms: -1x2 + 24x2 = 23x2 -4 + -5x + 23x2 = 8x + -24x2 + -8x + 24x2 Reorder the terms: -4 + -5x + 23x2 = 8x + -8x + -24x2 + 24x2 Combine like terms: 8x + -8x = 0 -4 + -5x + 23x2 = 0 + -24x2 + 24x2 -4 + -5x + 23x2 = -24x2 + 24x2 Combine like terms: -24x2 + 24x2 = 0 -4 + -5x + 23x2 = 0 Begin completing the square. Divide all terms by 23 the coefficient of the squared term: Divide each side by '23'. -0.1739130435 + -0.2173913043x + x2 = 0 Move the constant term to the right: Add '0.1739130435' to each side of the equation. -0.1739130435 + -0.2173913043x + 0.1739130435 + x2 = 0 + 0.1739130435 Reorder the terms: -0.1739130435 + 0.1739130435 + -0.2173913043x + x2 = 0 + 0.1739130435 Combine like terms: -0.1739130435 + 0.1739130435 = 0.0000000000 0.0000000000 + -0.2173913043x + x2 = 0 + 0.1739130435 -0.2173913043x + x2 = 0 + 0.1739130435 Combine like terms: 0 + 0.1739130435 = 0.1739130435 -0.2173913043x + x2 = 0.1739130435 The x term is -0.2173913043x. Take half its coefficient (-0.1086956522). Square it (0.01181474481) and add it to both sides. Add '0.01181474481' to each side of the equation. -0.2173913043x + 0.01181474481 + x2 = 0.1739130435 + 0.01181474481 Reorder the terms: 0.01181474481 + -0.2173913043x + x2 = 0.1739130435 + 0.01181474481 Combine like terms: 0.1739130435 + 0.01181474481 = 0.18572778831 0.01181474481 + -0.2173913043x + x2 = 0.18572778831 Factor a perfect square on the left side: (x + -0.1086956522)(x + -0.1086956522) = 0.18572778831 Calculate the square root of the right side: 0.43096147 Break this problem into two subproblems by setting (x + -0.1086956522) equal to 0.43096147 and -0.43096147.Subproblem 1
x + -0.1086956522 = 0.43096147 Simplifying x + -0.1086956522 = 0.43096147 Reorder the terms: -0.1086956522 + x = 0.43096147 Solving -0.1086956522 + x = 0.43096147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1086956522' to each side of the equation. -0.1086956522 + 0.1086956522 + x = 0.43096147 + 0.1086956522 Combine like terms: -0.1086956522 + 0.1086956522 = 0.0000000000 0.0000000000 + x = 0.43096147 + 0.1086956522 x = 0.43096147 + 0.1086956522 Combine like terms: 0.43096147 + 0.1086956522 = 0.5396571222 x = 0.5396571222 Simplifying x = 0.5396571222Subproblem 2
x + -0.1086956522 = -0.43096147 Simplifying x + -0.1086956522 = -0.43096147 Reorder the terms: -0.1086956522 + x = -0.43096147 Solving -0.1086956522 + x = -0.43096147 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1086956522' to each side of the equation. -0.1086956522 + 0.1086956522 + x = -0.43096147 + 0.1086956522 Combine like terms: -0.1086956522 + 0.1086956522 = 0.0000000000 0.0000000000 + x = -0.43096147 + 0.1086956522 x = -0.43096147 + 0.1086956522 Combine like terms: -0.43096147 + 0.1086956522 = -0.3222658178 x = -0.3222658178 Simplifying x = -0.3222658178Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5396571222, -0.3222658178}
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