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Simplifying 9x2 + 2476x + -246 = 258 Reorder the terms: -246 + 2476x + 9x2 = 258 Solving -246 + 2476x + 9x2 = 258 Solving for variable 'x'. Reorder the terms: -246 + -258 + 2476x + 9x2 = 258 + -258 Combine like terms: -246 + -258 = -504 -504 + 2476x + 9x2 = 258 + -258 Combine like terms: 258 + -258 = 0 -504 + 2476x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -56 + 275.1111111x + x2 = 0 Move the constant term to the right: Add '56' to each side of the equation. -56 + 275.1111111x + 56 + x2 = 0 + 56 Reorder the terms: -56 + 56 + 275.1111111x + x2 = 0 + 56 Combine like terms: -56 + 56 = 0 0 + 275.1111111x + x2 = 0 + 56 275.1111111x + x2 = 0 + 56 Combine like terms: 0 + 56 = 56 275.1111111x + x2 = 56 The x term is 275.1111111x. Take half its coefficient (137.5555556). Square it (18921.53088) and add it to both sides. Add '18921.53088' to each side of the equation. 275.1111111x + 18921.53088 + x2 = 56 + 18921.53088 Reorder the terms: 18921.53088 + 275.1111111x + x2 = 56 + 18921.53088 Combine like terms: 56 + 18921.53088 = 18977.53088 18921.53088 + 275.1111111x + x2 = 18977.53088 Factor a perfect square on the left side: (x + 137.5555556)(x + 137.5555556) = 18977.53088 Calculate the square root of the right side: 137.758959346 Break this problem into two subproblems by setting (x + 137.5555556) equal to 137.758959346 and -137.758959346.Subproblem 1
x + 137.5555556 = 137.758959346 Simplifying x + 137.5555556 = 137.758959346 Reorder the terms: 137.5555556 + x = 137.758959346 Solving 137.5555556 + x = 137.758959346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-137.5555556' to each side of the equation. 137.5555556 + -137.5555556 + x = 137.758959346 + -137.5555556 Combine like terms: 137.5555556 + -137.5555556 = 0.0000000 0.0000000 + x = 137.758959346 + -137.5555556 x = 137.758959346 + -137.5555556 Combine like terms: 137.758959346 + -137.5555556 = 0.203403746 x = 0.203403746 Simplifying x = 0.203403746Subproblem 2
x + 137.5555556 = -137.758959346 Simplifying x + 137.5555556 = -137.758959346 Reorder the terms: 137.5555556 + x = -137.758959346 Solving 137.5555556 + x = -137.758959346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-137.5555556' to each side of the equation. 137.5555556 + -137.5555556 + x = -137.758959346 + -137.5555556 Combine like terms: 137.5555556 + -137.5555556 = 0.0000000 0.0000000 + x = -137.758959346 + -137.5555556 x = -137.758959346 + -137.5555556 Combine like terms: -137.758959346 + -137.5555556 = -275.314514946 x = -275.314514946 Simplifying x = -275.314514946Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.203403746, -275.314514946}
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