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Simplifying 325 = 9x + x2 Solving 325 = 9x + x2 Solving for variable 'x'. Reorder the terms: 325 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 325 + -9x + -1x2 = 0 + x2 + -1x2 325 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 325 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -325 + 9x + x2 = 0 Move the constant term to the right: Add '325' to each side of the equation. -325 + 9x + 325 + x2 = 0 + 325 Reorder the terms: -325 + 325 + 9x + x2 = 0 + 325 Combine like terms: -325 + 325 = 0 0 + 9x + x2 = 0 + 325 9x + x2 = 0 + 325 Combine like terms: 0 + 325 = 325 9x + x2 = 325 The x term is 9x. Take half its coefficient (4.5). Square it (20.25) and add it to both sides. Add '20.25' to each side of the equation. 9x + 20.25 + x2 = 325 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 325 + 20.25 Combine like terms: 325 + 20.25 = 345.25 20.25 + 9x + x2 = 345.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 345.25 Calculate the square root of the right side: 18.580904176 Break this problem into two subproblems by setting (x + 4.5) equal to 18.580904176 and -18.580904176.Subproblem 1
x + 4.5 = 18.580904176 Simplifying x + 4.5 = 18.580904176 Reorder the terms: 4.5 + x = 18.580904176 Solving 4.5 + x = 18.580904176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = 18.580904176 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 18.580904176 + -4.5 x = 18.580904176 + -4.5 Combine like terms: 18.580904176 + -4.5 = 14.080904176 x = 14.080904176 Simplifying x = 14.080904176Subproblem 2
x + 4.5 = -18.580904176 Simplifying x + 4.5 = -18.580904176 Reorder the terms: 4.5 + x = -18.580904176 Solving 4.5 + x = -18.580904176 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4.5' to each side of the equation. 4.5 + -4.5 + x = -18.580904176 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -18.580904176 + -4.5 x = -18.580904176 + -4.5 Combine like terms: -18.580904176 + -4.5 = -23.080904176 x = -23.080904176 Simplifying x = -23.080904176Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.080904176, -23.080904176}
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