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Simplifying 27x2 + -51x + -26 = 0 Reorder the terms: -26 + -51x + 27x2 = 0 Solving -26 + -51x + 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'. -0.962962963 + -1.888888889x + x2 = 0 Move the constant term to the right: Add '0.962962963' to each side of the equation. -0.962962963 + -1.888888889x + 0.962962963 + x2 = 0 + 0.962962963 Reorder the terms: -0.962962963 + 0.962962963 + -1.888888889x + x2 = 0 + 0.962962963 Combine like terms: -0.962962963 + 0.962962963 = 0.000000000 0.000000000 + -1.888888889x + x2 = 0 + 0.962962963 -1.888888889x + x2 = 0 + 0.962962963 Combine like terms: 0 + 0.962962963 = 0.962962963 -1.888888889x + x2 = 0.962962963 The x term is -1.888888889x. Take half its coefficient (-0.9444444445). Square it (0.8919753087) and add it to both sides. Add '0.8919753087' to each side of the equation. -1.888888889x + 0.8919753087 + x2 = 0.962962963 + 0.8919753087 Reorder the terms: 0.8919753087 + -1.888888889x + x2 = 0.962962963 + 0.8919753087 Combine like terms: 0.962962963 + 0.8919753087 = 1.8549382717 0.8919753087 + -1.888888889x + x2 = 1.8549382717 Factor a perfect square on the left side: (x + -0.9444444445)(x + -0.9444444445) = 1.8549382717 Calculate the square root of the right side: 1.361961186 Break this problem into two subproblems by setting (x + -0.9444444445) equal to 1.361961186 and -1.361961186.Subproblem 1
x + -0.9444444445 = 1.361961186 Simplifying x + -0.9444444445 = 1.361961186 Reorder the terms: -0.9444444445 + x = 1.361961186 Solving -0.9444444445 + x = 1.361961186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = 1.361961186 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = 1.361961186 + 0.9444444445 x = 1.361961186 + 0.9444444445 Combine like terms: 1.361961186 + 0.9444444445 = 2.3064056305 x = 2.3064056305 Simplifying x = 2.3064056305Subproblem 2
x + -0.9444444445 = -1.361961186 Simplifying x + -0.9444444445 = -1.361961186 Reorder the terms: -0.9444444445 + x = -1.361961186 Solving -0.9444444445 + x = -1.361961186 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.9444444445' to each side of the equation. -0.9444444445 + 0.9444444445 + x = -1.361961186 + 0.9444444445 Combine like terms: -0.9444444445 + 0.9444444445 = 0.0000000000 0.0000000000 + x = -1.361961186 + 0.9444444445 x = -1.361961186 + 0.9444444445 Combine like terms: -1.361961186 + 0.9444444445 = -0.4175167415 x = -0.4175167415 Simplifying x = -0.4175167415Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.3064056305, -0.4175167415}
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