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Simplifying 7x2 + -4x + -1903608 = 0 Reorder the terms: -1903608 + -4x + 7x2 = 0 Solving -1903608 + -4x + 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'. -271944 + -0.5714285714x + x2 = 0 Move the constant term to the right: Add '271944' to each side of the equation. -271944 + -0.5714285714x + 271944 + x2 = 0 + 271944 Reorder the terms: -271944 + 271944 + -0.5714285714x + x2 = 0 + 271944 Combine like terms: -271944 + 271944 = 0 0 + -0.5714285714x + x2 = 0 + 271944 -0.5714285714x + x2 = 0 + 271944 Combine like terms: 0 + 271944 = 271944 -0.5714285714x + x2 = 271944 The x term is -0.5714285714x. Take half its coefficient (-0.2857142857). Square it (0.08163265305) and add it to both sides. Add '0.08163265305' to each side of the equation. -0.5714285714x + 0.08163265305 + x2 = 271944 + 0.08163265305 Reorder the terms: 0.08163265305 + -0.5714285714x + x2 = 271944 + 0.08163265305 Combine like terms: 271944 + 0.08163265305 = 271944.08163265305 0.08163265305 + -0.5714285714x + x2 = 271944.08163265305 Factor a perfect square on the left side: (x + -0.2857142857)(x + -0.2857142857) = 271944.08163265305 Calculate the square root of the right side: 521.482580373 Break this problem into two subproblems by setting (x + -0.2857142857) equal to 521.482580373 and -521.482580373.Subproblem 1
x + -0.2857142857 = 521.482580373 Simplifying x + -0.2857142857 = 521.482580373 Reorder the terms: -0.2857142857 + x = 521.482580373 Solving -0.2857142857 + x = 521.482580373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = 521.482580373 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = 521.482580373 + 0.2857142857 x = 521.482580373 + 0.2857142857 Combine like terms: 521.482580373 + 0.2857142857 = 521.7682946587 x = 521.7682946587 Simplifying x = 521.7682946587Subproblem 2
x + -0.2857142857 = -521.482580373 Simplifying x + -0.2857142857 = -521.482580373 Reorder the terms: -0.2857142857 + x = -521.482580373 Solving -0.2857142857 + x = -521.482580373 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.2857142857' to each side of the equation. -0.2857142857 + 0.2857142857 + x = -521.482580373 + 0.2857142857 Combine like terms: -0.2857142857 + 0.2857142857 = 0.0000000000 0.0000000000 + x = -521.482580373 + 0.2857142857 x = -521.482580373 + 0.2857142857 Combine like terms: -521.482580373 + 0.2857142857 = -521.1968660873 x = -521.1968660873 Simplifying x = -521.1968660873Solution
The solution to the problem is based on the solutions from the subproblems. x = {521.7682946587, -521.1968660873}
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