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Simplifying 6x(x + -5) + 4x(5x + -6) + 3x + 4 = 0 Reorder the terms: 6x(-5 + x) + 4x(5x + -6) + 3x + 4 = 0 (-5 * 6x + x * 6x) + 4x(5x + -6) + 3x + 4 = 0 (-30x + 6x2) + 4x(5x + -6) + 3x + 4 = 0 Reorder the terms: -30x + 6x2 + 4x(-6 + 5x) + 3x + 4 = 0 -30x + 6x2 + (-6 * 4x + 5x * 4x) + 3x + 4 = 0 -30x + 6x2 + (-24x + 20x2) + 3x + 4 = 0 Reorder the terms: 4 + -30x + -24x + 3x + 6x2 + 20x2 = 0 Combine like terms: -30x + -24x = -54x 4 + -54x + 3x + 6x2 + 20x2 = 0 Combine like terms: -54x + 3x = -51x 4 + -51x + 6x2 + 20x2 = 0 Combine like terms: 6x2 + 20x2 = 26x2 4 + -51x + 26x2 = 0 Solving 4 + -51x + 26x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 26 the coefficient of the squared term: Divide each side by '26'. 0.1538461538 + -1.961538462x + x2 = 0 Move the constant term to the right: Add '-0.1538461538' to each side of the equation. 0.1538461538 + -1.961538462x + -0.1538461538 + x2 = 0 + -0.1538461538 Reorder the terms: 0.1538461538 + -0.1538461538 + -1.961538462x + x2 = 0 + -0.1538461538 Combine like terms: 0.1538461538 + -0.1538461538 = 0.0000000000 0.0000000000 + -1.961538462x + x2 = 0 + -0.1538461538 -1.961538462x + x2 = 0 + -0.1538461538 Combine like terms: 0 + -0.1538461538 = -0.1538461538 -1.961538462x + x2 = -0.1538461538 The x term is -1.961538462x. Take half its coefficient (-0.980769231). Square it (0.9619082845) and add it to both sides. Add '0.9619082845' to each side of the equation. -1.961538462x + 0.9619082845 + x2 = -0.1538461538 + 0.9619082845 Reorder the terms: 0.9619082845 + -1.961538462x + x2 = -0.1538461538 + 0.9619082845 Combine like terms: -0.1538461538 + 0.9619082845 = 0.8080621307 0.9619082845 + -1.961538462x + x2 = 0.8080621307 Factor a perfect square on the left side: (x + -0.980769231)(x + -0.980769231) = 0.8080621307 Calculate the square root of the right side: 0.898922761 Break this problem into two subproblems by setting (x + -0.980769231) equal to 0.898922761 and -0.898922761.Subproblem 1
x + -0.980769231 = 0.898922761 Simplifying x + -0.980769231 = 0.898922761 Reorder the terms: -0.980769231 + x = 0.898922761 Solving -0.980769231 + x = 0.898922761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.980769231' to each side of the equation. -0.980769231 + 0.980769231 + x = 0.898922761 + 0.980769231 Combine like terms: -0.980769231 + 0.980769231 = 0.000000000 0.000000000 + x = 0.898922761 + 0.980769231 x = 0.898922761 + 0.980769231 Combine like terms: 0.898922761 + 0.980769231 = 1.879691992 x = 1.879691992 Simplifying x = 1.879691992Subproblem 2
x + -0.980769231 = -0.898922761 Simplifying x + -0.980769231 = -0.898922761 Reorder the terms: -0.980769231 + x = -0.898922761 Solving -0.980769231 + x = -0.898922761 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.980769231' to each side of the equation. -0.980769231 + 0.980769231 + x = -0.898922761 + 0.980769231 Combine like terms: -0.980769231 + 0.980769231 = 0.000000000 0.000000000 + x = -0.898922761 + 0.980769231 x = -0.898922761 + 0.980769231 Combine like terms: -0.898922761 + 0.980769231 = 0.08184647 x = 0.08184647 Simplifying x = 0.08184647Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.879691992, 0.08184647}
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