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Simplifying 9x + -1(5x + 1) + -1(2 + 8x)(7x + -5) + 10x = 0 Reorder the terms: 9x + -1(1 + 5x) + -1(2 + 8x)(7x + -5) + 10x = 0 9x + (1 * -1 + 5x * -1) + -1(2 + 8x)(7x + -5) + 10x = 0 9x + (-1 + -5x) + -1(2 + 8x)(7x + -5) + 10x = 0 Reorder the terms: 9x + -1 + -5x + -1(2 + 8x)(-5 + 7x) + 10x = 0 Multiply (2 + 8x) * (-5 + 7x) 9x + -1 + -5x + -1(2(-5 + 7x) + 8x * (-5 + 7x)) + 10x = 0 9x + -1 + -5x + -1((-5 * 2 + 7x * 2) + 8x * (-5 + 7x)) + 10x = 0 9x + -1 + -5x + -1((-10 + 14x) + 8x * (-5 + 7x)) + 10x = 0 9x + -1 + -5x + -1(-10 + 14x + (-5 * 8x + 7x * 8x)) + 10x = 0 9x + -1 + -5x + -1(-10 + 14x + (-40x + 56x2)) + 10x = 0 Combine like terms: 14x + -40x = -26x 9x + -1 + -5x + -1(-10 + -26x + 56x2) + 10x = 0 9x + -1 + -5x + (-10 * -1 + -26x * -1 + 56x2 * -1) + 10x = 0 9x + -1 + -5x + (10 + 26x + -56x2) + 10x = 0 Reorder the terms: -1 + 10 + 9x + -5x + 26x + 10x + -56x2 = 0 Combine like terms: -1 + 10 = 9 9 + 9x + -5x + 26x + 10x + -56x2 = 0 Combine like terms: 9x + -5x = 4x 9 + 4x + 26x + 10x + -56x2 = 0 Combine like terms: 4x + 26x = 30x 9 + 30x + 10x + -56x2 = 0 Combine like terms: 30x + 10x = 40x 9 + 40x + -56x2 = 0 Solving 9 + 40x + -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'. -0.1607142857 + -0.7142857143x + x2 = 0 Move the constant term to the right: Add '0.1607142857' to each side of the equation. -0.1607142857 + -0.7142857143x + 0.1607142857 + x2 = 0 + 0.1607142857 Reorder the terms: -0.1607142857 + 0.1607142857 + -0.7142857143x + x2 = 0 + 0.1607142857 Combine like terms: -0.1607142857 + 0.1607142857 = 0.0000000000 0.0000000000 + -0.7142857143x + x2 = 0 + 0.1607142857 -0.7142857143x + x2 = 0 + 0.1607142857 Combine like terms: 0 + 0.1607142857 = 0.1607142857 -0.7142857143x + x2 = 0.1607142857 The x term is -0.7142857143x. Take half its coefficient (-0.3571428572). Square it (0.1275510204) and add it to both sides. Add '0.1275510204' to each side of the equation. -0.7142857143x + 0.1275510204 + x2 = 0.1607142857 + 0.1275510204 Reorder the terms: 0.1275510204 + -0.7142857143x + x2 = 0.1607142857 + 0.1275510204 Combine like terms: 0.1607142857 + 0.1275510204 = 0.2882653061 0.1275510204 + -0.7142857143x + x2 = 0.2882653061 Factor a perfect square on the left side: (x + -0.3571428572)(x + -0.3571428572) = 0.2882653061 Calculate the square root of the right side: 0.536903442 Break this problem into two subproblems by setting (x + -0.3571428572) equal to 0.536903442 and -0.536903442.Subproblem 1
x + -0.3571428572 = 0.536903442 Simplifying x + -0.3571428572 = 0.536903442 Reorder the terms: -0.3571428572 + x = 0.536903442 Solving -0.3571428572 + x = 0.536903442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = 0.536903442 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = 0.536903442 + 0.3571428572 x = 0.536903442 + 0.3571428572 Combine like terms: 0.536903442 + 0.3571428572 = 0.8940462992 x = 0.8940462992 Simplifying x = 0.8940462992Subproblem 2
x + -0.3571428572 = -0.536903442 Simplifying x + -0.3571428572 = -0.536903442 Reorder the terms: -0.3571428572 + x = -0.536903442 Solving -0.3571428572 + x = -0.536903442 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.3571428572' to each side of the equation. -0.3571428572 + 0.3571428572 + x = -0.536903442 + 0.3571428572 Combine like terms: -0.3571428572 + 0.3571428572 = 0.0000000000 0.0000000000 + x = -0.536903442 + 0.3571428572 x = -0.536903442 + 0.3571428572 Combine like terms: -0.536903442 + 0.3571428572 = -0.1797605848 x = -0.1797605848 Simplifying x = -0.1797605848Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.8940462992, -0.1797605848}
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