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Simplifying (3x + -4)(x + -9) = 5 Reorder the terms: (-4 + 3x)(x + -9) = 5 Reorder the terms: (-4 + 3x)(-9 + x) = 5 Multiply (-4 + 3x) * (-9 + x) (-4(-9 + x) + 3x * (-9 + x)) = 5 ((-9 * -4 + x * -4) + 3x * (-9 + x)) = 5 ((36 + -4x) + 3x * (-9 + x)) = 5 (36 + -4x + (-9 * 3x + x * 3x)) = 5 (36 + -4x + (-27x + 3x2)) = 5 Combine like terms: -4x + -27x = -31x (36 + -31x + 3x2) = 5 Solving 36 + -31x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: 36 + -5 + -31x + 3x2 = 5 + -5 Combine like terms: 36 + -5 = 31 31 + -31x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 31 + -31x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 10.33333333 + -10.33333333x + x2 = 0 Move the constant term to the right: Add '-10.33333333' to each side of the equation. 10.33333333 + -10.33333333x + -10.33333333 + x2 = 0 + -10.33333333 Reorder the terms: 10.33333333 + -10.33333333 + -10.33333333x + x2 = 0 + -10.33333333 Combine like terms: 10.33333333 + -10.33333333 = 0.00000000 0.00000000 + -10.33333333x + x2 = 0 + -10.33333333 -10.33333333x + x2 = 0 + -10.33333333 Combine like terms: 0 + -10.33333333 = -10.33333333 -10.33333333x + x2 = -10.33333333 The x term is -10.33333333x. Take half its coefficient (-5.166666665). Square it (26.69444443) and add it to both sides. Add '26.69444443' to each side of the equation. -10.33333333x + 26.69444443 + x2 = -10.33333333 + 26.69444443 Reorder the terms: 26.69444443 + -10.33333333x + x2 = -10.33333333 + 26.69444443 Combine like terms: -10.33333333 + 26.69444443 = 16.3611111 26.69444443 + -10.33333333x + x2 = 16.3611111 Factor a perfect square on the left side: (x + -5.166666665)(x + -5.166666665) = 16.3611111 Calculate the square root of the right side: 4.044887032 Break this problem into two subproblems by setting (x + -5.166666665) equal to 4.044887032 and -4.044887032.Subproblem 1
x + -5.166666665 = 4.044887032 Simplifying x + -5.166666665 = 4.044887032 Reorder the terms: -5.166666665 + x = 4.044887032 Solving -5.166666665 + x = 4.044887032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = 4.044887032 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = 4.044887032 + 5.166666665 x = 4.044887032 + 5.166666665 Combine like terms: 4.044887032 + 5.166666665 = 9.211553697 x = 9.211553697 Simplifying x = 9.211553697Subproblem 2
x + -5.166666665 = -4.044887032 Simplifying x + -5.166666665 = -4.044887032 Reorder the terms: -5.166666665 + x = -4.044887032 Solving -5.166666665 + x = -4.044887032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5.166666665' to each side of the equation. -5.166666665 + 5.166666665 + x = -4.044887032 + 5.166666665 Combine like terms: -5.166666665 + 5.166666665 = 0.000000000 0.000000000 + x = -4.044887032 + 5.166666665 x = -4.044887032 + 5.166666665 Combine like terms: -4.044887032 + 5.166666665 = 1.121779633 x = 1.121779633 Simplifying x = 1.121779633Solution
The solution to the problem is based on the solutions from the subproblems. x = {9.211553697, 1.121779633}
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