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Simplifying (23x)(4x + -1) = 8 Remove parenthesis around (23x) 23x(4x + -1) = 8 Reorder the terms: 23x(-1 + 4x) = 8 (-1 * 23x + 4x * 23x) = 8 (-23x + 92x2) = 8 Solving -23x + 92x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -23x + 92x2 = 8 + -8 Combine like terms: 8 + -8 = 0 -8 + -23x + 92x2 = 0 Begin completing the square. Divide all terms by 92 the coefficient of the squared term: Divide each side by '92'. -0.08695652174 + -0.25x + x2 = 0 Move the constant term to the right: Add '0.08695652174' to each side of the equation. -0.08695652174 + -0.25x + 0.08695652174 + x2 = 0 + 0.08695652174 Reorder the terms: -0.08695652174 + 0.08695652174 + -0.25x + x2 = 0 + 0.08695652174 Combine like terms: -0.08695652174 + 0.08695652174 = 0.00000000000 0.00000000000 + -0.25x + x2 = 0 + 0.08695652174 -0.25x + x2 = 0 + 0.08695652174 Combine like terms: 0 + 0.08695652174 = 0.08695652174 -0.25x + x2 = 0.08695652174 The x term is -0.25x. Take half its coefficient (-0.125). Square it (0.015625) and add it to both sides. Add '0.015625' to each side of the equation. -0.25x + 0.015625 + x2 = 0.08695652174 + 0.015625 Reorder the terms: 0.015625 + -0.25x + x2 = 0.08695652174 + 0.015625 Combine like terms: 0.08695652174 + 0.015625 = 0.10258152174 0.015625 + -0.25x + x2 = 0.10258152174 Factor a perfect square on the left side: (x + -0.125)(x + -0.125) = 0.10258152174 Calculate the square root of the right side: 0.320283502 Break this problem into two subproblems by setting (x + -0.125) equal to 0.320283502 and -0.320283502.Subproblem 1
x + -0.125 = 0.320283502 Simplifying x + -0.125 = 0.320283502 Reorder the terms: -0.125 + x = 0.320283502 Solving -0.125 + x = 0.320283502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = 0.320283502 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = 0.320283502 + 0.125 x = 0.320283502 + 0.125 Combine like terms: 0.320283502 + 0.125 = 0.445283502 x = 0.445283502 Simplifying x = 0.445283502Subproblem 2
x + -0.125 = -0.320283502 Simplifying x + -0.125 = -0.320283502 Reorder the terms: -0.125 + x = -0.320283502 Solving -0.125 + x = -0.320283502 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.125' to each side of the equation. -0.125 + 0.125 + x = -0.320283502 + 0.125 Combine like terms: -0.125 + 0.125 = 0.000 0.000 + x = -0.320283502 + 0.125 x = -0.320283502 + 0.125 Combine like terms: -0.320283502 + 0.125 = -0.195283502 x = -0.195283502 Simplifying x = -0.195283502Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.445283502, -0.195283502}
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