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Simplifying 49x2 + 1024 + -448x + 8x(32 + -7x) + -320 = 0 49x2 + 1024 + -448x + (32 * 8x + -7x * 8x) + -320 = 0 49x2 + 1024 + -448x + (256x + -56x2) + -320 = 0 Reorder the terms: 1024 + -320 + -448x + 256x + 49x2 + -56x2 = 0 Combine like terms: 1024 + -320 = 704 704 + -448x + 256x + 49x2 + -56x2 = 0 Combine like terms: -448x + 256x = -192x 704 + -192x + 49x2 + -56x2 = 0 Combine like terms: 49x2 + -56x2 = -7x2 704 + -192x + -7x2 = 0 Solving 704 + -192x + -7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -7 the coefficient of the squared term: Divide each side by '-7'. -100.5714286 + 27.42857143x + x2 = 0 Move the constant term to the right: Add '100.5714286' to each side of the equation. -100.5714286 + 27.42857143x + 100.5714286 + x2 = 0 + 100.5714286 Reorder the terms: -100.5714286 + 100.5714286 + 27.42857143x + x2 = 0 + 100.5714286 Combine like terms: -100.5714286 + 100.5714286 = 0.0000000 0.0000000 + 27.42857143x + x2 = 0 + 100.5714286 27.42857143x + x2 = 0 + 100.5714286 Combine like terms: 0 + 100.5714286 = 100.5714286 27.42857143x + x2 = 100.5714286 The x term is 27.42857143x. Take half its coefficient (13.71428572). Square it (188.0816328) and add it to both sides. Add '188.0816328' to each side of the equation. 27.42857143x + 188.0816328 + x2 = 100.5714286 + 188.0816328 Reorder the terms: 188.0816328 + 27.42857143x + x2 = 100.5714286 + 188.0816328 Combine like terms: 100.5714286 + 188.0816328 = 288.6530614 188.0816328 + 27.42857143x + x2 = 288.6530614 Factor a perfect square on the left side: (x + 13.71428572)(x + 13.71428572) = 288.6530614 Calculate the square root of the right side: 16.989792859 Break this problem into two subproblems by setting (x + 13.71428572) equal to 16.989792859 and -16.989792859.Subproblem 1
x + 13.71428572 = 16.989792859 Simplifying x + 13.71428572 = 16.989792859 Reorder the terms: 13.71428572 + x = 16.989792859 Solving 13.71428572 + x = 16.989792859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.71428572' to each side of the equation. 13.71428572 + -13.71428572 + x = 16.989792859 + -13.71428572 Combine like terms: 13.71428572 + -13.71428572 = 0.00000000 0.00000000 + x = 16.989792859 + -13.71428572 x = 16.989792859 + -13.71428572 Combine like terms: 16.989792859 + -13.71428572 = 3.275507139 x = 3.275507139 Simplifying x = 3.275507139Subproblem 2
x + 13.71428572 = -16.989792859 Simplifying x + 13.71428572 = -16.989792859 Reorder the terms: 13.71428572 + x = -16.989792859 Solving 13.71428572 + x = -16.989792859 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13.71428572' to each side of the equation. 13.71428572 + -13.71428572 + x = -16.989792859 + -13.71428572 Combine like terms: 13.71428572 + -13.71428572 = 0.00000000 0.00000000 + x = -16.989792859 + -13.71428572 x = -16.989792859 + -13.71428572 Combine like terms: -16.989792859 + -13.71428572 = -30.704078579 x = -30.704078579 Simplifying x = -30.704078579Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.275507139, -30.704078579}
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