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Simplifying 9x + -1(5x + 1) + -1(2 + 8x(7x + -5)) + 9x = 0 Reorder the terms: 9x + -1(1 + 5x) + -1(2 + 8x(7x + -5)) + 9x = 0 9x + (1 * -1 + 5x * -1) + -1(2 + 8x(7x + -5)) + 9x = 0 9x + (-1 + -5x) + -1(2 + 8x(7x + -5)) + 9x = 0 Reorder the terms: 9x + -1 + -5x + -1(2 + 8x(-5 + 7x)) + 9x = 0 9x + -1 + -5x + -1(2 + (-5 * 8x + 7x * 8x)) + 9x = 0 9x + -1 + -5x + -1(2 + (-40x + 56x2)) + 9x = 0 9x + -1 + -5x + (2 * -1 + -40x * -1 + 56x2 * -1) + 9x = 0 9x + -1 + -5x + (-2 + 40x + -56x2) + 9x = 0 Reorder the terms: -1 + -2 + 9x + -5x + 40x + 9x + -56x2 = 0 Combine like terms: -1 + -2 = -3 -3 + 9x + -5x + 40x + 9x + -56x2 = 0 Combine like terms: 9x + -5x = 4x -3 + 4x + 40x + 9x + -56x2 = 0 Combine like terms: 4x + 40x = 44x -3 + 44x + 9x + -56x2 = 0 Combine like terms: 44x + 9x = 53x -3 + 53x + -56x2 = 0 Solving -3 + 53x + -56x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -56 the coefficient of the squared term: Divide each side by '-56'. 0.05357142857 + -0.9464285714x + x2 = 0 Move the constant term to the right: Add '-0.05357142857' to each side of the equation. 0.05357142857 + -0.9464285714x + -0.05357142857 + x2 = 0 + -0.05357142857 Reorder the terms: 0.05357142857 + -0.05357142857 + -0.9464285714x + x2 = 0 + -0.05357142857 Combine like terms: 0.05357142857 + -0.05357142857 = 0.00000000000 0.00000000000 + -0.9464285714x + x2 = 0 + -0.05357142857 -0.9464285714x + x2 = 0 + -0.05357142857 Combine like terms: 0 + -0.05357142857 = -0.05357142857 -0.9464285714x + x2 = -0.05357142857 The x term is -0.9464285714x. Take half its coefficient (-0.4732142857). Square it (0.2239317602) and add it to both sides. Add '0.2239317602' to each side of the equation. -0.9464285714x + 0.2239317602 + x2 = -0.05357142857 + 0.2239317602 Reorder the terms: 0.2239317602 + -0.9464285714x + x2 = -0.05357142857 + 0.2239317602 Combine like terms: -0.05357142857 + 0.2239317602 = 0.17036033163 0.2239317602 + -0.9464285714x + x2 = 0.17036033163 Factor a perfect square on the left side: (x + -0.4732142857)(x + -0.4732142857) = 0.17036033163 Calculate the square root of the right side: 0.412747298 Break this problem into two subproblems by setting (x + -0.4732142857) equal to 0.412747298 and -0.412747298.Subproblem 1
x + -0.4732142857 = 0.412747298 Simplifying x + -0.4732142857 = 0.412747298 Reorder the terms: -0.4732142857 + x = 0.412747298 Solving -0.4732142857 + x = 0.412747298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4732142857' to each side of the equation. -0.4732142857 + 0.4732142857 + x = 0.412747298 + 0.4732142857 Combine like terms: -0.4732142857 + 0.4732142857 = 0.0000000000 0.0000000000 + x = 0.412747298 + 0.4732142857 x = 0.412747298 + 0.4732142857 Combine like terms: 0.412747298 + 0.4732142857 = 0.8859615837 x = 0.8859615837 Simplifying x = 0.8859615837Subproblem 2
x + -0.4732142857 = -0.412747298 Simplifying x + -0.4732142857 = -0.412747298 Reorder the terms: -0.4732142857 + x = -0.412747298 Solving -0.4732142857 + x = -0.412747298 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4732142857' to each side of the equation. -0.4732142857 + 0.4732142857 + x = -0.412747298 + 0.4732142857 Combine like terms: -0.4732142857 + 0.4732142857 = 0.0000000000 0.0000000000 + x = -0.412747298 + 0.4732142857 x = -0.412747298 + 0.4732142857 Combine like terms: -0.412747298 + 0.4732142857 = 0.0604669877 x = 0.0604669877 Simplifying x = 0.0604669877Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8859615837, 0.0604669877}
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