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Simplifying 2x2 + 9x + -225 = 0 Reorder the terms: -225 + 9x + 2x2 = 0 Solving -225 + 9x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -112.5 + 4.5x + x2 = 0 Move the constant term to the right: Add '112.5' to each side of the equation. -112.5 + 4.5x + 112.5 + x2 = 0 + 112.5 Reorder the terms: -112.5 + 112.5 + 4.5x + x2 = 0 + 112.5 Combine like terms: -112.5 + 112.5 = 0.0 0.0 + 4.5x + x2 = 0 + 112.5 4.5x + x2 = 0 + 112.5 Combine like terms: 0 + 112.5 = 112.5 4.5x + x2 = 112.5 The x term is 4.5x. Take half its coefficient (2.25). Square it (5.0625) and add it to both sides. Add '5.0625' to each side of the equation. 4.5x + 5.0625 + x2 = 112.5 + 5.0625 Reorder the terms: 5.0625 + 4.5x + x2 = 112.5 + 5.0625 Combine like terms: 112.5 + 5.0625 = 117.5625 5.0625 + 4.5x + x2 = 117.5625 Factor a perfect square on the left side: (x + 2.25)(x + 2.25) = 117.5625 Calculate the square root of the right side: 10.842624221 Break this problem into two subproblems by setting (x + 2.25) equal to 10.842624221 and -10.842624221.Subproblem 1
x + 2.25 = 10.842624221 Simplifying x + 2.25 = 10.842624221 Reorder the terms: 2.25 + x = 10.842624221 Solving 2.25 + x = 10.842624221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = 10.842624221 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = 10.842624221 + -2.25 x = 10.842624221 + -2.25 Combine like terms: 10.842624221 + -2.25 = 8.592624221 x = 8.592624221 Simplifying x = 8.592624221Subproblem 2
x + 2.25 = -10.842624221 Simplifying x + 2.25 = -10.842624221 Reorder the terms: 2.25 + x = -10.842624221 Solving 2.25 + x = -10.842624221 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.25' to each side of the equation. 2.25 + -2.25 + x = -10.842624221 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + x = -10.842624221 + -2.25 x = -10.842624221 + -2.25 Combine like terms: -10.842624221 + -2.25 = -13.092624221 x = -13.092624221 Simplifying x = -13.092624221Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.592624221, -13.092624221}
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