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Simplifying 78x2 + 5x + -58 = 0 Reorder the terms: -58 + 5x + 78x2 = 0 Solving -58 + 5x + 78x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 78 the coefficient of the squared term: Divide each side by '78'. -0.7435897436 + 0.0641025641x + x2 = 0 Move the constant term to the right: Add '0.7435897436' to each side of the equation. -0.7435897436 + 0.0641025641x + 0.7435897436 + x2 = 0 + 0.7435897436 Reorder the terms: -0.7435897436 + 0.7435897436 + 0.0641025641x + x2 = 0 + 0.7435897436 Combine like terms: -0.7435897436 + 0.7435897436 = 0.0000000000 0.0000000000 + 0.0641025641x + x2 = 0 + 0.7435897436 0.0641025641x + x2 = 0 + 0.7435897436 Combine like terms: 0 + 0.7435897436 = 0.7435897436 0.0641025641x + x2 = 0.7435897436 The x term is 0.0641025641x. Take half its coefficient (0.03205128205). Square it (0.001027284681) and add it to both sides. Add '0.001027284681' to each side of the equation. 0.0641025641x + 0.001027284681 + x2 = 0.7435897436 + 0.001027284681 Reorder the terms: 0.001027284681 + 0.0641025641x + x2 = 0.7435897436 + 0.001027284681 Combine like terms: 0.7435897436 + 0.001027284681 = 0.744617028281 0.001027284681 + 0.0641025641x + x2 = 0.744617028281 Factor a perfect square on the left side: (x + 0.03205128205)(x + 0.03205128205) = 0.744617028281 Calculate the square root of the right side: 0.862911947 Break this problem into two subproblems by setting (x + 0.03205128205) equal to 0.862911947 and -0.862911947.Subproblem 1
x + 0.03205128205 = 0.862911947 Simplifying x + 0.03205128205 = 0.862911947 Reorder the terms: 0.03205128205 + x = 0.862911947 Solving 0.03205128205 + x = 0.862911947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03205128205' to each side of the equation. 0.03205128205 + -0.03205128205 + x = 0.862911947 + -0.03205128205 Combine like terms: 0.03205128205 + -0.03205128205 = 0.00000000000 0.00000000000 + x = 0.862911947 + -0.03205128205 x = 0.862911947 + -0.03205128205 Combine like terms: 0.862911947 + -0.03205128205 = 0.83086066495 x = 0.83086066495 Simplifying x = 0.83086066495Subproblem 2
x + 0.03205128205 = -0.862911947 Simplifying x + 0.03205128205 = -0.862911947 Reorder the terms: 0.03205128205 + x = -0.862911947 Solving 0.03205128205 + x = -0.862911947 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.03205128205' to each side of the equation. 0.03205128205 + -0.03205128205 + x = -0.862911947 + -0.03205128205 Combine like terms: 0.03205128205 + -0.03205128205 = 0.00000000000 0.00000000000 + x = -0.862911947 + -0.03205128205 x = -0.862911947 + -0.03205128205 Combine like terms: -0.862911947 + -0.03205128205 = -0.89496322905 x = -0.89496322905 Simplifying x = -0.89496322905Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.83086066495, -0.89496322905}
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