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Simplifying 2x + 7x + -3(4x + -9) + 2x + -4 = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Reorder the terms: 2x + 7x + -3(-9 + 4x) + 2x + -4 = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x 2x + 7x + (-9 * -3 + 4x * -3) + 2x + -4 = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x 2x + 7x + (27 + -12x) + 2x + -4 = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Reorder the terms: 27 + -4 + 2x + 7x + -12x + 2x = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Combine like terms: 27 + -4 = 23 23 + 2x + 7x + -12x + 2x = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Combine like terms: 2x + 7x = 9x 23 + 9x + -12x + 2x = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Combine like terms: 9x + -12x = -3x 23 + -3x + 2x = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Combine like terms: -3x + 2x = -1x 23 + -1x = 11x(x + 2) + -3(x + -9) + 4x + -1 + 2x Reorder the terms: 23 + -1x = 11x(2 + x) + -3(x + -9) + 4x + -1 + 2x 23 + -1x = (2 * 11x + x * 11x) + -3(x + -9) + 4x + -1 + 2x 23 + -1x = (22x + 11x2) + -3(x + -9) + 4x + -1 + 2x Reorder the terms: 23 + -1x = 22x + 11x2 + -3(-9 + x) + 4x + -1 + 2x 23 + -1x = 22x + 11x2 + (-9 * -3 + x * -3) + 4x + -1 + 2x 23 + -1x = 22x + 11x2 + (27 + -3x) + 4x + -1 + 2x Reorder the terms: 23 + -1x = 27 + -1 + 22x + -3x + 4x + 2x + 11x2 Combine like terms: 27 + -1 = 26 23 + -1x = 26 + 22x + -3x + 4x + 2x + 11x2 Combine like terms: 22x + -3x = 19x 23 + -1x = 26 + 19x + 4x + 2x + 11x2 Combine like terms: 19x + 4x = 23x 23 + -1x = 26 + 23x + 2x + 11x2 Combine like terms: 23x + 2x = 25x 23 + -1x = 26 + 25x + 11x2 Solving 23 + -1x = 26 + 25x + 11x2 Solving for variable 'x'. Reorder the terms: 23 + -26 + -1x + -25x + -11x2 = 26 + 25x + 11x2 + -26 + -25x + -11x2 Combine like terms: 23 + -26 = -3 -3 + -1x + -25x + -11x2 = 26 + 25x + 11x2 + -26 + -25x + -11x2 Combine like terms: -1x + -25x = -26x -3 + -26x + -11x2 = 26 + 25x + 11x2 + -26 + -25x + -11x2 Reorder the terms: -3 + -26x + -11x2 = 26 + -26 + 25x + -25x + 11x2 + -11x2 Combine like terms: 26 + -26 = 0 -3 + -26x + -11x2 = 0 + 25x + -25x + 11x2 + -11x2 -3 + -26x + -11x2 = 25x + -25x + 11x2 + -11x2 Combine like terms: 25x + -25x = 0 -3 + -26x + -11x2 = 0 + 11x2 + -11x2 -3 + -26x + -11x2 = 11x2 + -11x2 Combine like terms: 11x2 + -11x2 = 0 -3 + -26x + -11x2 = 0 Factor out the Greatest Common Factor (GCF), '-1'. -1(3 + 26x + 11x2) = 0 Ignore the factor -1.Subproblem 1
Set the factor '(3 + 26x + 11x2)' equal to zero and attempt to solve: Simplifying 3 + 26x + 11x2 = 0 Solving 3 + 26x + 11x2 = 0 Begin completing the square. Divide all terms by 11 the coefficient of the squared term: Divide each side by '11'. 0.2727272727 + 2.363636364x + x2 = 0 Move the constant term to the right: Add '-0.2727272727' to each side of the equation. 0.2727272727 + 2.363636364x + -0.2727272727 + x2 = 0 + -0.2727272727 Reorder the terms: 0.2727272727 + -0.2727272727 + 2.363636364x + x2 = 0 + -0.2727272727 Combine like terms: 0.2727272727 + -0.2727272727 = 0.0000000000 0.0000000000 + 2.363636364x + x2 = 0 + -0.2727272727 2.363636364x + x2 = 0 + -0.2727272727 Combine like terms: 0 + -0.2727272727 = -0.2727272727 2.363636364x + x2 = -0.2727272727 The x term is 2.363636364x. Take half its coefficient (1.181818182). Square it (1.396694215) and add it to both sides. Add '1.396694215' to each side of the equation. 2.363636364x + 1.396694215 + x2 = -0.2727272727 + 1.396694215 Reorder the terms: 1.396694215 + 2.363636364x + x2 = -0.2727272727 + 1.396694215 Combine like terms: -0.2727272727 + 1.396694215 = 1.1239669423 1.396694215 + 2.363636364x + x2 = 1.1239669423 Factor a perfect square on the left side: (x + 1.181818182)(x + 1.181818182) = 1.1239669423 Calculate the square root of the right side: 1.060173072 Break this problem into two subproblems by setting (x + 1.181818182) equal to 1.060173072 and -1.060173072.Subproblem 1
x + 1.181818182 = 1.060173072 Simplifying x + 1.181818182 = 1.060173072 Reorder the terms: 1.181818182 + x = 1.060173072 Solving 1.181818182 + x = 1.060173072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.181818182' to each side of the equation. 1.181818182 + -1.181818182 + x = 1.060173072 + -1.181818182 Combine like terms: 1.181818182 + -1.181818182 = 0.000000000 0.000000000 + x = 1.060173072 + -1.181818182 x = 1.060173072 + -1.181818182 Combine like terms: 1.060173072 + -1.181818182 = -0.12164511 x = -0.12164511 Simplifying x = -0.12164511Subproblem 2
x + 1.181818182 = -1.060173072 Simplifying x + 1.181818182 = -1.060173072 Reorder the terms: 1.181818182 + x = -1.060173072 Solving 1.181818182 + x = -1.060173072 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.181818182' to each side of the equation. 1.181818182 + -1.181818182 + x = -1.060173072 + -1.181818182 Combine like terms: 1.181818182 + -1.181818182 = 0.000000000 0.000000000 + x = -1.060173072 + -1.181818182 x = -1.060173072 + -1.181818182 Combine like terms: -1.060173072 + -1.181818182 = -2.241991254 x = -2.241991254 Simplifying x = -2.241991254Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.12164511, -2.241991254}Solution
x = {-0.12164511, -2.241991254}
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