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Simplifying 2840x2 + 5525x + -83496 = 0 Reorder the terms: -83496 + 5525x + 2840x2 = 0 Solving -83496 + 5525x + 2840x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2840 the coefficient of the squared term: Divide each side by '2840'. -29.4 + 1.945422535x + x2 = 0 Move the constant term to the right: Add '29.4' to each side of the equation. -29.4 + 1.945422535x + 29.4 + x2 = 0 + 29.4 Reorder the terms: -29.4 + 29.4 + 1.945422535x + x2 = 0 + 29.4 Combine like terms: -29.4 + 29.4 = 0.0 0.0 + 1.945422535x + x2 = 0 + 29.4 1.945422535x + x2 = 0 + 29.4 Combine like terms: 0 + 29.4 = 29.4 1.945422535x + x2 = 29.4 The x term is 1.945422535x. Take half its coefficient (0.9727112675). Square it (0.9461672099) and add it to both sides. Add '0.9461672099' to each side of the equation. 1.945422535x + 0.9461672099 + x2 = 29.4 + 0.9461672099 Reorder the terms: 0.9461672099 + 1.945422535x + x2 = 29.4 + 0.9461672099 Combine like terms: 29.4 + 0.9461672099 = 30.3461672099 0.9461672099 + 1.945422535x + x2 = 30.3461672099 Factor a perfect square on the left side: (x + 0.9727112675)(x + 0.9727112675) = 30.3461672099 Calculate the square root of the right side: 5.508735536 Break this problem into two subproblems by setting (x + 0.9727112675) equal to 5.508735536 and -5.508735536.Subproblem 1
x + 0.9727112675 = 5.508735536 Simplifying x + 0.9727112675 = 5.508735536 Reorder the terms: 0.9727112675 + x = 5.508735536 Solving 0.9727112675 + x = 5.508735536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9727112675' to each side of the equation. 0.9727112675 + -0.9727112675 + x = 5.508735536 + -0.9727112675 Combine like terms: 0.9727112675 + -0.9727112675 = 0.0000000000 0.0000000000 + x = 5.508735536 + -0.9727112675 x = 5.508735536 + -0.9727112675 Combine like terms: 5.508735536 + -0.9727112675 = 4.5360242685 x = 4.5360242685 Simplifying x = 4.5360242685Subproblem 2
x + 0.9727112675 = -5.508735536 Simplifying x + 0.9727112675 = -5.508735536 Reorder the terms: 0.9727112675 + x = -5.508735536 Solving 0.9727112675 + x = -5.508735536 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9727112675' to each side of the equation. 0.9727112675 + -0.9727112675 + x = -5.508735536 + -0.9727112675 Combine like terms: 0.9727112675 + -0.9727112675 = 0.0000000000 0.0000000000 + x = -5.508735536 + -0.9727112675 x = -5.508735536 + -0.9727112675 Combine like terms: -5.508735536 + -0.9727112675 = -6.4814468035 x = -6.4814468035 Simplifying x = -6.4814468035Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.5360242685, -6.4814468035}
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