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Simplifying -19.72(12.6x + -54)(3.8x + 2) = 0 Reorder the terms: -19.72(-54 + 12.6x)(3.8x + 2) = 0 Reorder the terms: -19.72(-54 + 12.6x)(2 + 3.8x) = 0 Multiply (-54 + 12.6x) * (2 + 3.8x) -19.72(-54(2 + 3.8x) + 12.6x * (2 + 3.8x)) = 0 -19.72((2 * -54 + 3.8x * -54) + 12.6x * (2 + 3.8x)) = 0 -19.72((-108 + -205.2x) + 12.6x * (2 + 3.8x)) = 0 -19.72(-108 + -205.2x + (2 * 12.6x + 3.8x * 12.6x)) = 0 -19.72(-108 + -205.2x + (25.2x + 47.88x2)) = 0 Combine like terms: -205.2x + 25.2x = -180x -19.72(-108 + -180x + 47.88x2) = 0 (-108 * -19.72 + -180x * -19.72 + 47.88x2 * -19.72) = 0 (2129.76 + 3549.6x + -944.1936x2) = 0 Solving 2129.76 + 3549.6x + -944.1936x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -944.1936 the coefficient of the squared term: Divide each side by '-944.1936'. -2.255639098 + -3.759398496x + x2 = 0 Move the constant term to the right: Add '2.255639098' to each side of the equation. -2.255639098 + -3.759398496x + 2.255639098 + x2 = 0 + 2.255639098 Reorder the terms: -2.255639098 + 2.255639098 + -3.759398496x + x2 = 0 + 2.255639098 Combine like terms: -2.255639098 + 2.255639098 = 0.000000000 0.000000000 + -3.759398496x + x2 = 0 + 2.255639098 -3.759398496x + x2 = 0 + 2.255639098 Combine like terms: 0 + 2.255639098 = 2.255639098 -3.759398496x + x2 = 2.255639098 The x term is -3.759398496x. Take half its coefficient (-1.879699248). Square it (3.533269263) and add it to both sides. Add '3.533269263' to each side of the equation. -3.759398496x + 3.533269263 + x2 = 2.255639098 + 3.533269263 Reorder the terms: 3.533269263 + -3.759398496x + x2 = 2.255639098 + 3.533269263 Combine like terms: 2.255639098 + 3.533269263 = 5.788908361 3.533269263 + -3.759398496x + x2 = 5.788908361 Factor a perfect square on the left side: (x + -1.879699248)(x + -1.879699248) = 5.788908361 Calculate the square root of the right side: 2.406015038 Break this problem into two subproblems by setting (x + -1.879699248) equal to 2.406015038 and -2.406015038.Subproblem 1
x + -1.879699248 = 2.406015038 Simplifying x + -1.879699248 = 2.406015038 Reorder the terms: -1.879699248 + x = 2.406015038 Solving -1.879699248 + x = 2.406015038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.879699248' to each side of the equation. -1.879699248 + 1.879699248 + x = 2.406015038 + 1.879699248 Combine like terms: -1.879699248 + 1.879699248 = 0.000000000 0.000000000 + x = 2.406015038 + 1.879699248 x = 2.406015038 + 1.879699248 Combine like terms: 2.406015038 + 1.879699248 = 4.285714286 x = 4.285714286 Simplifying x = 4.285714286Subproblem 2
x + -1.879699248 = -2.406015038 Simplifying x + -1.879699248 = -2.406015038 Reorder the terms: -1.879699248 + x = -2.406015038 Solving -1.879699248 + x = -2.406015038 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.879699248' to each side of the equation. -1.879699248 + 1.879699248 + x = -2.406015038 + 1.879699248 Combine like terms: -1.879699248 + 1.879699248 = 0.000000000 0.000000000 + x = -2.406015038 + 1.879699248 x = -2.406015038 + 1.879699248 Combine like terms: -2.406015038 + 1.879699248 = -0.52631579 x = -0.52631579 Simplifying x = -0.52631579Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.285714286, -0.52631579}
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