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Simplifying 5x(4 + -1x) = 9 + -1(x + -6) (4 * 5x + -1x * 5x) = 9 + -1(x + -6) (20x + -5x2) = 9 + -1(x + -6) Reorder the terms: 20x + -5x2 = 9 + -1(-6 + x) 20x + -5x2 = 9 + (-6 * -1 + x * -1) 20x + -5x2 = 9 + (6 + -1x) Combine like terms: 9 + 6 = 15 20x + -5x2 = 15 + -1x Solving 20x + -5x2 = 15 + -1x Solving for variable 'x'. Reorder the terms: -15 + 20x + x + -5x2 = 15 + -1x + -15 + x Combine like terms: 20x + x = 21x -15 + 21x + -5x2 = 15 + -1x + -15 + x Reorder the terms: -15 + 21x + -5x2 = 15 + -15 + -1x + x Combine like terms: 15 + -15 = 0 -15 + 21x + -5x2 = 0 + -1x + x -15 + 21x + -5x2 = -1x + x Combine like terms: -1x + x = 0 -15 + 21x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 3 + -4.2x + x2 = 0 Move the constant term to the right: Add '-3' to each side of the equation. 3 + -4.2x + -3 + x2 = 0 + -3 Reorder the terms: 3 + -3 + -4.2x + x2 = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -4.2x + x2 = 0 + -3 -4.2x + x2 = 0 + -3 Combine like terms: 0 + -3 = -3 -4.2x + x2 = -3 The x term is -4.2x. Take half its coefficient (-2.1). Square it (4.41) and add it to both sides. Add '4.41' to each side of the equation. -4.2x + 4.41 + x2 = -3 + 4.41 Reorder the terms: 4.41 + -4.2x + x2 = -3 + 4.41 Combine like terms: -3 + 4.41 = 1.41 4.41 + -4.2x + x2 = 1.41 Factor a perfect square on the left side: (x + -2.1)(x + -2.1) = 1.41 Calculate the square root of the right side: 1.187434209 Break this problem into two subproblems by setting (x + -2.1) equal to 1.187434209 and -1.187434209.Subproblem 1
x + -2.1 = 1.187434209 Simplifying x + -2.1 = 1.187434209 Reorder the terms: -2.1 + x = 1.187434209 Solving -2.1 + x = 1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = 1.187434209 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = 1.187434209 + 2.1 x = 1.187434209 + 2.1 Combine like terms: 1.187434209 + 2.1 = 3.287434209 x = 3.287434209 Simplifying x = 3.287434209Subproblem 2
x + -2.1 = -1.187434209 Simplifying x + -2.1 = -1.187434209 Reorder the terms: -2.1 + x = -1.187434209 Solving -2.1 + x = -1.187434209 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.1' to each side of the equation. -2.1 + 2.1 + x = -1.187434209 + 2.1 Combine like terms: -2.1 + 2.1 = 0.0 0.0 + x = -1.187434209 + 2.1 x = -1.187434209 + 2.1 Combine like terms: -1.187434209 + 2.1 = 0.912565791 x = 0.912565791 Simplifying x = 0.912565791Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.287434209, 0.912565791}
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