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Simplifying x(0.18x + -1) = 5 Reorder the terms: x(-1 + 0.18x) = 5 (-1 * x + 0.18x * x) = 5 (-1x + 0.18x2) = 5 Solving -1x + 0.18x2 = 5 Solving for variable 'x'. Reorder the terms: -5 + -1x + 0.18x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -5 + -1x + 0.18x2 = 0 Begin completing the square. Divide all terms by 0.18 the coefficient of the squared term: Divide each side by '0.18'. -27.77777778 + -5.555555556x + x2 = 0 Move the constant term to the right: Add '27.77777778' to each side of the equation. -27.77777778 + -5.555555556x + 27.77777778 + x2 = 0 + 27.77777778 Reorder the terms: -27.77777778 + 27.77777778 + -5.555555556x + x2 = 0 + 27.77777778 Combine like terms: -27.77777778 + 27.77777778 = 0.00000000 0.00000000 + -5.555555556x + x2 = 0 + 27.77777778 -5.555555556x + x2 = 0 + 27.77777778 Combine like terms: 0 + 27.77777778 = 27.77777778 -5.555555556x + x2 = 27.77777778 The x term is -5.555555556x. Take half its coefficient (-2.777777778). Square it (7.716049384) and add it to both sides. Add '7.716049384' to each side of the equation. -5.555555556x + 7.716049384 + x2 = 27.77777778 + 7.716049384 Reorder the terms: 7.716049384 + -5.555555556x + x2 = 27.77777778 + 7.716049384 Combine like terms: 27.77777778 + 7.716049384 = 35.493827164 7.716049384 + -5.555555556x + x2 = 35.493827164 Factor a perfect square on the left side: (x + -2.777777778)(x + -2.777777778) = 35.493827164 Calculate the square root of the right side: 5.957669608 Break this problem into two subproblems by setting (x + -2.777777778) equal to 5.957669608 and -5.957669608.Subproblem 1
x + -2.777777778 = 5.957669608 Simplifying x + -2.777777778 = 5.957669608 Reorder the terms: -2.777777778 + x = 5.957669608 Solving -2.777777778 + x = 5.957669608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = 5.957669608 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = 5.957669608 + 2.777777778 x = 5.957669608 + 2.777777778 Combine like terms: 5.957669608 + 2.777777778 = 8.735447386 x = 8.735447386 Simplifying x = 8.735447386Subproblem 2
x + -2.777777778 = -5.957669608 Simplifying x + -2.777777778 = -5.957669608 Reorder the terms: -2.777777778 + x = -5.957669608 Solving -2.777777778 + x = -5.957669608 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.777777778' to each side of the equation. -2.777777778 + 2.777777778 + x = -5.957669608 + 2.777777778 Combine like terms: -2.777777778 + 2.777777778 = 0.000000000 0.000000000 + x = -5.957669608 + 2.777777778 x = -5.957669608 + 2.777777778 Combine like terms: -5.957669608 + 2.777777778 = -3.17989183 x = -3.17989183 Simplifying x = -3.17989183Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.735447386, -3.17989183}
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