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Simplifying 9x2 = -5x + 8 Reorder the terms: 9x2 = 8 + -5x Solving 9x2 = 8 + -5x Solving for variable 'x'. Reorder the terms: -8 + 5x + 9x2 = 8 + -5x + -8 + 5x Reorder the terms: -8 + 5x + 9x2 = 8 + -8 + -5x + 5x Combine like terms: 8 + -8 = 0 -8 + 5x + 9x2 = 0 + -5x + 5x -8 + 5x + 9x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -8 + 5x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.5555555556x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.5555555556x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.5555555556x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.5555555556x + x2 = 0 + 0.8888888889 0.5555555556x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.5555555556x + x2 = 0.8888888889 The x term is 0.5555555556x. Take half its coefficient (0.2777777778). Square it (0.07716049384) and add it to both sides. Add '0.07716049384' to each side of the equation. 0.5555555556x + 0.07716049384 + x2 = 0.8888888889 + 0.07716049384 Reorder the terms: 0.07716049384 + 0.5555555556x + x2 = 0.8888888889 + 0.07716049384 Combine like terms: 0.8888888889 + 0.07716049384 = 0.96604938274 0.07716049384 + 0.5555555556x + x2 = 0.96604938274 Factor a perfect square on the left side: (x + 0.2777777778)(x + 0.2777777778) = 0.96604938274 Calculate the square root of the right side: 0.982878112 Break this problem into two subproblems by setting (x + 0.2777777778) equal to 0.982878112 and -0.982878112.Subproblem 1
x + 0.2777777778 = 0.982878112 Simplifying x + 0.2777777778 = 0.982878112 Reorder the terms: 0.2777777778 + x = 0.982878112 Solving 0.2777777778 + x = 0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = 0.982878112 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = 0.982878112 + -0.2777777778 x = 0.982878112 + -0.2777777778 Combine like terms: 0.982878112 + -0.2777777778 = 0.7051003342 x = 0.7051003342 Simplifying x = 0.7051003342Subproblem 2
x + 0.2777777778 = -0.982878112 Simplifying x + 0.2777777778 = -0.982878112 Reorder the terms: 0.2777777778 + x = -0.982878112 Solving 0.2777777778 + x = -0.982878112 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2777777778' to each side of the equation. 0.2777777778 + -0.2777777778 + x = -0.982878112 + -0.2777777778 Combine like terms: 0.2777777778 + -0.2777777778 = 0.0000000000 0.0000000000 + x = -0.982878112 + -0.2777777778 x = -0.982878112 + -0.2777777778 Combine like terms: -0.982878112 + -0.2777777778 = -1.2606558898 x = -1.2606558898 Simplifying x = -1.2606558898Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7051003342, -1.2606558898}
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