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Simplifying 4(x + 5) * 3 + -91 = 6x(9 + -1x) Reorder the terms: 4(5 + x) * 3 + -91 = 6x(9 + -1x) Reorder the terms for easier multiplication: 4 * 3(5 + x) + -91 = 6x(9 + -1x) Multiply 4 * 3 12(5 + x) + -91 = 6x(9 + -1x) (5 * 12 + x * 12) + -91 = 6x(9 + -1x) (60 + 12x) + -91 = 6x(9 + -1x) Reorder the terms: 60 + -91 + 12x = 6x(9 + -1x) Combine like terms: 60 + -91 = -31 -31 + 12x = 6x(9 + -1x) -31 + 12x = (9 * 6x + -1x * 6x) -31 + 12x = (54x + -6x2) Solving -31 + 12x = 54x + -6x2 Solving for variable 'x'. Combine like terms: 12x + -54x = -42x -31 + -42x + 6x2 = 54x + -6x2 + -54x + 6x2 Reorder the terms: -31 + -42x + 6x2 = 54x + -54x + -6x2 + 6x2 Combine like terms: 54x + -54x = 0 -31 + -42x + 6x2 = 0 + -6x2 + 6x2 -31 + -42x + 6x2 = -6x2 + 6x2 Combine like terms: -6x2 + 6x2 = 0 -31 + -42x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -5.166666667 + -7x + x2 = 0 Move the constant term to the right: Add '5.166666667' to each side of the equation. -5.166666667 + -7x + 5.166666667 + x2 = 0 + 5.166666667 Reorder the terms: -5.166666667 + 5.166666667 + -7x + x2 = 0 + 5.166666667 Combine like terms: -5.166666667 + 5.166666667 = 0.000000000 0.000000000 + -7x + x2 = 0 + 5.166666667 -7x + x2 = 0 + 5.166666667 Combine like terms: 0 + 5.166666667 = 5.166666667 -7x + x2 = 5.166666667 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = 5.166666667 + 12.25 Reorder the terms: 12.25 + -7x + x2 = 5.166666667 + 12.25 Combine like terms: 5.166666667 + 12.25 = 17.416666667 12.25 + -7x + x2 = 17.416666667 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 17.416666667 Calculate the square root of the right side: 4.173328009 Break this problem into two subproblems by setting (x + -3.5) equal to 4.173328009 and -4.173328009.Subproblem 1
x + -3.5 = 4.173328009 Simplifying x + -3.5 = 4.173328009 Reorder the terms: -3.5 + x = 4.173328009 Solving -3.5 + x = 4.173328009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 4.173328009 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 4.173328009 + 3.5 x = 4.173328009 + 3.5 Combine like terms: 4.173328009 + 3.5 = 7.673328009 x = 7.673328009 Simplifying x = 7.673328009Subproblem 2
x + -3.5 = -4.173328009 Simplifying x + -3.5 = -4.173328009 Reorder the terms: -3.5 + x = -4.173328009 Solving -3.5 + x = -4.173328009 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -4.173328009 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -4.173328009 + 3.5 x = -4.173328009 + 3.5 Combine like terms: -4.173328009 + 3.5 = -0.673328009 x = -0.673328009 Simplifying x = -0.673328009Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.673328009, -0.673328009}
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