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Simplifying (-5x2 + 3x) + -1(6x2 + 7x + -4) = 0 Reorder the terms: (3x + -5x2) + -1(6x2 + 7x + -4) = 0 Remove parenthesis around (3x + -5x2) 3x + -5x2 + -1(6x2 + 7x + -4) = 0 Reorder the terms: 3x + -5x2 + -1(-4 + 7x + 6x2) = 0 3x + -5x2 + (-4 * -1 + 7x * -1 + 6x2 * -1) = 0 3x + -5x2 + (4 + -7x + -6x2) = 0 Reorder the terms: 4 + 3x + -7x + -5x2 + -6x2 = 0 Combine like terms: 3x + -7x = -4x 4 + -4x + -5x2 + -6x2 = 0 Combine like terms: -5x2 + -6x2 = -11x2 4 + -4x + -11x2 = 0 Solving 4 + -4x + -11x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -11 the coefficient of the squared term: Divide each side by '-11'. -0.3636363636 + 0.3636363636x + x2 = 0 Move the constant term to the right: Add '0.3636363636' to each side of the equation. -0.3636363636 + 0.3636363636x + 0.3636363636 + x2 = 0 + 0.3636363636 Reorder the terms: -0.3636363636 + 0.3636363636 + 0.3636363636x + x2 = 0 + 0.3636363636 Combine like terms: -0.3636363636 + 0.3636363636 = 0.0000000000 0.0000000000 + 0.3636363636x + x2 = 0 + 0.3636363636 0.3636363636x + x2 = 0 + 0.3636363636 Combine like terms: 0 + 0.3636363636 = 0.3636363636 0.3636363636x + x2 = 0.3636363636 The x term is 0.3636363636x. Take half its coefficient (0.1818181818). Square it (0.03305785123) and add it to both sides. Add '0.03305785123' to each side of the equation. 0.3636363636x + 0.03305785123 + x2 = 0.3636363636 + 0.03305785123 Reorder the terms: 0.03305785123 + 0.3636363636x + x2 = 0.3636363636 + 0.03305785123 Combine like terms: 0.3636363636 + 0.03305785123 = 0.39669421483 0.03305785123 + 0.3636363636x + x2 = 0.39669421483 Factor a perfect square on the left side: (x + 0.1818181818)(x + 0.1818181818) = 0.39669421483 Calculate the square root of the right side: 0.629836657 Break this problem into two subproblems by setting (x + 0.1818181818) equal to 0.629836657 and -0.629836657.Subproblem 1
x + 0.1818181818 = 0.629836657 Simplifying x + 0.1818181818 = 0.629836657 Reorder the terms: 0.1818181818 + x = 0.629836657 Solving 0.1818181818 + x = 0.629836657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = 0.629836657 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = 0.629836657 + -0.1818181818 x = 0.629836657 + -0.1818181818 Combine like terms: 0.629836657 + -0.1818181818 = 0.4480184752 x = 0.4480184752 Simplifying x = 0.4480184752Subproblem 2
x + 0.1818181818 = -0.629836657 Simplifying x + 0.1818181818 = -0.629836657 Reorder the terms: 0.1818181818 + x = -0.629836657 Solving 0.1818181818 + x = -0.629836657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1818181818' to each side of the equation. 0.1818181818 + -0.1818181818 + x = -0.629836657 + -0.1818181818 Combine like terms: 0.1818181818 + -0.1818181818 = 0.0000000000 0.0000000000 + x = -0.629836657 + -0.1818181818 x = -0.629836657 + -0.1818181818 Combine like terms: -0.629836657 + -0.1818181818 = -0.8116548388 x = -0.8116548388 Simplifying x = -0.8116548388Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4480184752, -0.8116548388}
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