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Simplifying 9x2 = 8 + -8x Solving 9x2 = 8 + -8x Solving for variable 'x'. Reorder the terms: -8 + 8x + 9x2 = 8 + -8x + -8 + 8x Reorder the terms: -8 + 8x + 9x2 = 8 + -8 + -8x + 8x Combine like terms: 8 + -8 = 0 -8 + 8x + 9x2 = 0 + -8x + 8x -8 + 8x + 9x2 = -8x + 8x Combine like terms: -8x + 8x = 0 -8 + 8x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.8888888889 + 0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.8888888889' to each side of the equation. -0.8888888889 + 0.8888888889x + 0.8888888889 + x2 = 0 + 0.8888888889 Reorder the terms: -0.8888888889 + 0.8888888889 + 0.8888888889x + x2 = 0 + 0.8888888889 Combine like terms: -0.8888888889 + 0.8888888889 = 0.0000000000 0.0000000000 + 0.8888888889x + x2 = 0 + 0.8888888889 0.8888888889x + x2 = 0 + 0.8888888889 Combine like terms: 0 + 0.8888888889 = 0.8888888889 0.8888888889x + x2 = 0.8888888889 The x term is 0.8888888889x. Take half its coefficient (0.4444444445). Square it (0.1975308642) and add it to both sides. Add '0.1975308642' to each side of the equation. 0.8888888889x + 0.1975308642 + x2 = 0.8888888889 + 0.1975308642 Reorder the terms: 0.1975308642 + 0.8888888889x + x2 = 0.8888888889 + 0.1975308642 Combine like terms: 0.8888888889 + 0.1975308642 = 1.0864197531 0.1975308642 + 0.8888888889x + x2 = 1.0864197531 Factor a perfect square on the left side: (x + 0.4444444445)(x + 0.4444444445) = 1.0864197531 Calculate the square root of the right side: 1.042314613 Break this problem into two subproblems by setting (x + 0.4444444445) equal to 1.042314613 and -1.042314613.Subproblem 1
x + 0.4444444445 = 1.042314613 Simplifying x + 0.4444444445 = 1.042314613 Reorder the terms: 0.4444444445 + x = 1.042314613 Solving 0.4444444445 + x = 1.042314613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = 1.042314613 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = 1.042314613 + -0.4444444445 x = 1.042314613 + -0.4444444445 Combine like terms: 1.042314613 + -0.4444444445 = 0.5978701685 x = 0.5978701685 Simplifying x = 0.5978701685Subproblem 2
x + 0.4444444445 = -1.042314613 Simplifying x + 0.4444444445 = -1.042314613 Reorder the terms: 0.4444444445 + x = -1.042314613 Solving 0.4444444445 + x = -1.042314613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4444444445' to each side of the equation. 0.4444444445 + -0.4444444445 + x = -1.042314613 + -0.4444444445 Combine like terms: 0.4444444445 + -0.4444444445 = 0.0000000000 0.0000000000 + x = -1.042314613 + -0.4444444445 x = -1.042314613 + -0.4444444445 Combine like terms: -1.042314613 + -0.4444444445 = -1.4867590575 x = -1.4867590575 Simplifying x = -1.4867590575Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5978701685, -1.4867590575}
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