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Simplifying 5x(9x + -20) = (11x + 5) Reorder the terms: 5x(-20 + 9x) = (11x + 5) (-20 * 5x + 9x * 5x) = (11x + 5) (-100x + 45x2) = (11x + 5) Reorder the terms: -100x + 45x2 = (5 + 11x) Remove parenthesis around (5 + 11x) -100x + 45x2 = 5 + 11x Solving -100x + 45x2 = 5 + 11x Solving for variable 'x'. Reorder the terms: -5 + -100x + -11x + 45x2 = 5 + 11x + -5 + -11x Combine like terms: -100x + -11x = -111x -5 + -111x + 45x2 = 5 + 11x + -5 + -11x Reorder the terms: -5 + -111x + 45x2 = 5 + -5 + 11x + -11x Combine like terms: 5 + -5 = 0 -5 + -111x + 45x2 = 0 + 11x + -11x -5 + -111x + 45x2 = 11x + -11x Combine like terms: 11x + -11x = 0 -5 + -111x + 45x2 = 0 Begin completing the square. Divide all terms by 45 the coefficient of the squared term: Divide each side by '45'. -0.1111111111 + -2.466666667x + x2 = 0 Move the constant term to the right: Add '0.1111111111' to each side of the equation. -0.1111111111 + -2.466666667x + 0.1111111111 + x2 = 0 + 0.1111111111 Reorder the terms: -0.1111111111 + 0.1111111111 + -2.466666667x + x2 = 0 + 0.1111111111 Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000 0.0000000000 + -2.466666667x + x2 = 0 + 0.1111111111 -2.466666667x + x2 = 0 + 0.1111111111 Combine like terms: 0 + 0.1111111111 = 0.1111111111 -2.466666667x + x2 = 0.1111111111 The x term is -2.466666667x. Take half its coefficient (-1.233333334). Square it (1.521111113) and add it to both sides. Add '1.521111113' to each side of the equation. -2.466666667x + 1.521111113 + x2 = 0.1111111111 + 1.521111113 Reorder the terms: 1.521111113 + -2.466666667x + x2 = 0.1111111111 + 1.521111113 Combine like terms: 0.1111111111 + 1.521111113 = 1.6322222241 1.521111113 + -2.466666667x + x2 = 1.6322222241 Factor a perfect square on the left side: (x + -1.233333334)(x + -1.233333334) = 1.6322222241 Calculate the square root of the right side: 1.277584527 Break this problem into two subproblems by setting (x + -1.233333334) equal to 1.277584527 and -1.277584527.Subproblem 1
x + -1.233333334 = 1.277584527 Simplifying x + -1.233333334 = 1.277584527 Reorder the terms: -1.233333334 + x = 1.277584527 Solving -1.233333334 + x = 1.277584527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.233333334' to each side of the equation. -1.233333334 + 1.233333334 + x = 1.277584527 + 1.233333334 Combine like terms: -1.233333334 + 1.233333334 = 0.000000000 0.000000000 + x = 1.277584527 + 1.233333334 x = 1.277584527 + 1.233333334 Combine like terms: 1.277584527 + 1.233333334 = 2.510917861 x = 2.510917861 Simplifying x = 2.510917861Subproblem 2
x + -1.233333334 = -1.277584527 Simplifying x + -1.233333334 = -1.277584527 Reorder the terms: -1.233333334 + x = -1.277584527 Solving -1.233333334 + x = -1.277584527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.233333334' to each side of the equation. -1.233333334 + 1.233333334 + x = -1.277584527 + 1.233333334 Combine like terms: -1.233333334 + 1.233333334 = 0.000000000 0.000000000 + x = -1.277584527 + 1.233333334 x = -1.277584527 + 1.233333334 Combine like terms: -1.277584527 + 1.233333334 = -0.044251193 x = -0.044251193 Simplifying x = -0.044251193Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.510917861, -0.044251193}
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