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Simplifying 9x2 + -8x = 8 Reorder the terms: -8x + 9x2 = 8 Solving -8x + 9x2 = 8 Solving for variable 'x'. Reorder the terms: -8 + -8x + 9x2 = 8 + -8 Combine like terms: 8 + -8 = 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 = 1.4867590575 x = 1.4867590575 Simplifying x = 1.4867590575Subproblem 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 = -0.5978701685 x = -0.5978701685 Simplifying x = -0.5978701685Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.4867590575, -0.5978701685}
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