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Simplifying 443697479 = 25x + x2 Solving 443697479 = 25x + x2 Solving for variable 'x'. Reorder the terms: 443697479 + -25x + -1x2 = 25x + -25x + x2 + -1x2 Combine like terms: 25x + -25x = 0 443697479 + -25x + -1x2 = 0 + x2 + -1x2 443697479 + -25x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 443697479 + -25x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -443697479 + 25x + x2 = 0 Move the constant term to the right: Add '443697479' to each side of the equation. -443697479 + 25x + 443697479 + x2 = 0 + 443697479 Reorder the terms: -443697479 + 443697479 + 25x + x2 = 0 + 443697479 Combine like terms: -443697479 + 443697479 = 0 0 + 25x + x2 = 0 + 443697479 25x + x2 = 0 + 443697479 Combine like terms: 0 + 443697479 = 443697479 25x + x2 = 443697479 The x term is 25x. Take half its coefficient (12.5). Square it (156.25) and add it to both sides. Add '156.25' to each side of the equation. 25x + 156.25 + x2 = 443697479 + 156.25 Reorder the terms: 156.25 + 25x + x2 = 443697479 + 156.25 Combine like terms: 443697479 + 156.25 = 443697635.25 156.25 + 25x + x2 = 443697635.25 Factor a perfect square on the left side: (x + 12.5)(x + 12.5) = 443697635.25 Calculate the square root of the right side: 21064.131485775 Break this problem into two subproblems by setting (x + 12.5) equal to 21064.131485775 and -21064.131485775.Subproblem 1
x + 12.5 = 21064.131485775 Simplifying x + 12.5 = 21064.131485775 Reorder the terms: 12.5 + x = 21064.131485775 Solving 12.5 + x = 21064.131485775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = 21064.131485775 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = 21064.131485775 + -12.5 x = 21064.131485775 + -12.5 Combine like terms: 21064.131485775 + -12.5 = 21051.631485775 x = 21051.631485775 Simplifying x = 21051.631485775Subproblem 2
x + 12.5 = -21064.131485775 Simplifying x + 12.5 = -21064.131485775 Reorder the terms: 12.5 + x = -21064.131485775 Solving 12.5 + x = -21064.131485775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-12.5' to each side of the equation. 12.5 + -12.5 + x = -21064.131485775 + -12.5 Combine like terms: 12.5 + -12.5 = 0.0 0.0 + x = -21064.131485775 + -12.5 x = -21064.131485775 + -12.5 Combine like terms: -21064.131485775 + -12.5 = -21076.631485775 x = -21076.631485775 Simplifying x = -21076.631485775Solution
The solution to the problem is based on the solutions from the subproblems. x = {21051.631485775, -21076.631485775}
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