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Simplifying 27x2 + -24x + -7 = 0 Reorder the terms: -7 + -24x + 27x2 = 0 Solving -7 + -24x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.2592592593 + -0.8888888889x + x2 = 0 Move the constant term to the right: Add '0.2592592593' to each side of the equation. -0.2592592593 + -0.8888888889x + 0.2592592593 + x2 = 0 + 0.2592592593 Reorder the terms: -0.2592592593 + 0.2592592593 + -0.8888888889x + x2 = 0 + 0.2592592593 Combine like terms: -0.2592592593 + 0.2592592593 = 0.0000000000 0.0000000000 + -0.8888888889x + x2 = 0 + 0.2592592593 -0.8888888889x + x2 = 0 + 0.2592592593 Combine like terms: 0 + 0.2592592593 = 0.2592592593 -0.8888888889x + x2 = 0.2592592593 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 = 0.2592592593 + 0.1975308642 Reorder the terms: 0.1975308642 + -0.8888888889x + x2 = 0.2592592593 + 0.1975308642 Combine like terms: 0.2592592593 + 0.1975308642 = 0.4567901235 0.1975308642 + -0.8888888889x + x2 = 0.4567901235 Factor a perfect square on the left side: (x + -0.4444444445)(x + -0.4444444445) = 0.4567901235 Calculate the square root of the right side: 0.675862503 Break this problem into two subproblems by setting (x + -0.4444444445) equal to 0.675862503 and -0.675862503.Subproblem 1
x + -0.4444444445 = 0.675862503 Simplifying x + -0.4444444445 = 0.675862503 Reorder the terms: -0.4444444445 + x = 0.675862503 Solving -0.4444444445 + x = 0.675862503 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 = 0.675862503 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = 0.675862503 + 0.4444444445 x = 0.675862503 + 0.4444444445 Combine like terms: 0.675862503 + 0.4444444445 = 1.1203069475 x = 1.1203069475 Simplifying x = 1.1203069475Subproblem 2
x + -0.4444444445 = -0.675862503 Simplifying x + -0.4444444445 = -0.675862503 Reorder the terms: -0.4444444445 + x = -0.675862503 Solving -0.4444444445 + x = -0.675862503 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 = -0.675862503 + 0.4444444445 Combine like terms: -0.4444444445 + 0.4444444445 = 0.0000000000 0.0000000000 + x = -0.675862503 + 0.4444444445 x = -0.675862503 + 0.4444444445 Combine like terms: -0.675862503 + 0.4444444445 = -0.2314180585 x = -0.2314180585 Simplifying x = -0.2314180585Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.1203069475, -0.2314180585}
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