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Simplifying (8x2 + -8x) + -1(-9x2 + -2x + 6) = 0 Reorder the terms: (-8x + 8x2) + -1(-9x2 + -2x + 6) = 0 Remove parenthesis around (-8x + 8x2) -8x + 8x2 + -1(-9x2 + -2x + 6) = 0 Reorder the terms: -8x + 8x2 + -1(6 + -2x + -9x2) = 0 -8x + 8x2 + (6 * -1 + -2x * -1 + -9x2 * -1) = 0 -8x + 8x2 + (-6 + 2x + 9x2) = 0 Reorder the terms: -6 + -8x + 2x + 8x2 + 9x2 = 0 Combine like terms: -8x + 2x = -6x -6 + -6x + 8x2 + 9x2 = 0 Combine like terms: 8x2 + 9x2 = 17x2 -6 + -6x + 17x2 = 0 Solving -6 + -6x + 17x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 17 the coefficient of the squared term: Divide each side by '17'. -0.3529411765 + -0.3529411765x + x2 = 0 Move the constant term to the right: Add '0.3529411765' to each side of the equation. -0.3529411765 + -0.3529411765x + 0.3529411765 + x2 = 0 + 0.3529411765 Reorder the terms: -0.3529411765 + 0.3529411765 + -0.3529411765x + x2 = 0 + 0.3529411765 Combine like terms: -0.3529411765 + 0.3529411765 = 0.0000000000 0.0000000000 + -0.3529411765x + x2 = 0 + 0.3529411765 -0.3529411765x + x2 = 0 + 0.3529411765 Combine like terms: 0 + 0.3529411765 = 0.3529411765 -0.3529411765x + x2 = 0.3529411765 The x term is -0.3529411765x. Take half its coefficient (-0.1764705883). Square it (0.03114186853) and add it to both sides. Add '0.03114186853' to each side of the equation. -0.3529411765x + 0.03114186853 + x2 = 0.3529411765 + 0.03114186853 Reorder the terms: 0.03114186853 + -0.3529411765x + x2 = 0.3529411765 + 0.03114186853 Combine like terms: 0.3529411765 + 0.03114186853 = 0.38408304503 0.03114186853 + -0.3529411765x + x2 = 0.38408304503 Factor a perfect square on the left side: (x + -0.1764705883)(x + -0.1764705883) = 0.38408304503 Calculate the square root of the right side: 0.619744338 Break this problem into two subproblems by setting (x + -0.1764705883) equal to 0.619744338 and -0.619744338.Subproblem 1
x + -0.1764705883 = 0.619744338 Simplifying x + -0.1764705883 = 0.619744338 Reorder the terms: -0.1764705883 + x = 0.619744338 Solving -0.1764705883 + x = 0.619744338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + x = 0.619744338 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = 0.619744338 + 0.1764705883 x = 0.619744338 + 0.1764705883 Combine like terms: 0.619744338 + 0.1764705883 = 0.7962149263 x = 0.7962149263 Simplifying x = 0.7962149263Subproblem 2
x + -0.1764705883 = -0.619744338 Simplifying x + -0.1764705883 = -0.619744338 Reorder the terms: -0.1764705883 + x = -0.619744338 Solving -0.1764705883 + x = -0.619744338 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1764705883' to each side of the equation. -0.1764705883 + 0.1764705883 + x = -0.619744338 + 0.1764705883 Combine like terms: -0.1764705883 + 0.1764705883 = 0.0000000000 0.0000000000 + x = -0.619744338 + 0.1764705883 x = -0.619744338 + 0.1764705883 Combine like terms: -0.619744338 + 0.1764705883 = -0.4432737497 x = -0.4432737497 Simplifying x = -0.4432737497Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.7962149263, -0.4432737497}
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