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Simplifying 5x(9 + -1x) + -1(17 + -3x) = -3(2 + -5x) (9 * 5x + -1x * 5x) + -1(17 + -3x) = -3(2 + -5x) (45x + -5x2) + -1(17 + -3x) = -3(2 + -5x) 45x + -5x2 + (17 * -1 + -3x * -1) = -3(2 + -5x) 45x + -5x2 + (-17 + 3x) = -3(2 + -5x) Reorder the terms: -17 + 45x + 3x + -5x2 = -3(2 + -5x) Combine like terms: 45x + 3x = 48x -17 + 48x + -5x2 = -3(2 + -5x) -17 + 48x + -5x2 = (2 * -3 + -5x * -3) -17 + 48x + -5x2 = (-6 + 15x) Solving -17 + 48x + -5x2 = -6 + 15x Solving for variable 'x'. Reorder the terms: -17 + 6 + 48x + -15x + -5x2 = -6 + 15x + 6 + -15x Combine like terms: -17 + 6 = -11 -11 + 48x + -15x + -5x2 = -6 + 15x + 6 + -15x Combine like terms: 48x + -15x = 33x -11 + 33x + -5x2 = -6 + 15x + 6 + -15x Reorder the terms: -11 + 33x + -5x2 = -6 + 6 + 15x + -15x Combine like terms: -6 + 6 = 0 -11 + 33x + -5x2 = 0 + 15x + -15x -11 + 33x + -5x2 = 15x + -15x Combine like terms: 15x + -15x = 0 -11 + 33x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 2.2 + -6.6x + x2 = 0 Move the constant term to the right: Add '-2.2' to each side of the equation. 2.2 + -6.6x + -2.2 + x2 = 0 + -2.2 Reorder the terms: 2.2 + -2.2 + -6.6x + x2 = 0 + -2.2 Combine like terms: 2.2 + -2.2 = 0.0 0.0 + -6.6x + x2 = 0 + -2.2 -6.6x + x2 = 0 + -2.2 Combine like terms: 0 + -2.2 = -2.2 -6.6x + x2 = -2.2 The x term is -6.6x. Take half its coefficient (-3.3). Square it (10.89) and add it to both sides. Add '10.89' to each side of the equation. -6.6x + 10.89 + x2 = -2.2 + 10.89 Reorder the terms: 10.89 + -6.6x + x2 = -2.2 + 10.89 Combine like terms: -2.2 + 10.89 = 8.69 10.89 + -6.6x + x2 = 8.69 Factor a perfect square on the left side: (x + -3.3)(x + -3.3) = 8.69 Calculate the square root of the right side: 2.947880595 Break this problem into two subproblems by setting (x + -3.3) equal to 2.947880595 and -2.947880595.Subproblem 1
x + -3.3 = 2.947880595 Simplifying x + -3.3 = 2.947880595 Reorder the terms: -3.3 + x = 2.947880595 Solving -3.3 + x = 2.947880595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = 2.947880595 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = 2.947880595 + 3.3 x = 2.947880595 + 3.3 Combine like terms: 2.947880595 + 3.3 = 6.247880595 x = 6.247880595 Simplifying x = 6.247880595Subproblem 2
x + -3.3 = -2.947880595 Simplifying x + -3.3 = -2.947880595 Reorder the terms: -3.3 + x = -2.947880595 Solving -3.3 + x = -2.947880595 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.3' to each side of the equation. -3.3 + 3.3 + x = -2.947880595 + 3.3 Combine like terms: -3.3 + 3.3 = 0.0 0.0 + x = -2.947880595 + 3.3 x = -2.947880595 + 3.3 Combine like terms: -2.947880595 + 3.3 = 0.352119405 x = 0.352119405 Simplifying x = 0.352119405Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.247880595, 0.352119405}
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