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Simplifying 0 = x2 + 9x + -25 Reorder the terms: 0 = -25 + 9x + x2 Solving 0 = -25 + 9x + x2 Solving for variable 'x'. Combine like terms: 0 + 25 = 25 25 + -9x + -1x2 = -25 + 9x + x2 + 25 + -9x + -1x2 Reorder the terms: 25 + -9x + -1x2 = -25 + 25 + 9x + -9x + x2 + -1x2 Combine like terms: -25 + 25 = 0 25 + -9x + -1x2 = 0 + 9x + -9x + x2 + -1x2 25 + -9x + -1x2 = 9x + -9x + x2 + -1x2 Combine like terms: 9x + -9x = 0 25 + -9x + -1x2 = 0 + x2 + -1x2 25 + -9x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 25 + -9x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -25 + 9x + x2 = 0 Move the constant term to the right: Add '25' to each side of the equation. -25 + 9x + 25 + x2 = 0 + 25 Reorder the terms: -25 + 25 + 9x + x2 = 0 + 25 Combine like terms: -25 + 25 = 0 0 + 9x + x2 = 0 + 25 9x + x2 = 0 + 25 Combine like terms: 0 + 25 = 25 9x + x2 = 25 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 = 25 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 25 + 20.25 Combine like terms: 25 + 20.25 = 45.25 20.25 + 9x + x2 = 45.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 45.25 Calculate the square root of the right side: 6.726812024 Break this problem into two subproblems by setting (x + 4.5) equal to 6.726812024 and -6.726812024.Subproblem 1
x + 4.5 = 6.726812024 Simplifying x + 4.5 = 6.726812024 Reorder the terms: 4.5 + x = 6.726812024 Solving 4.5 + x = 6.726812024 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 = 6.726812024 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 6.726812024 + -4.5 x = 6.726812024 + -4.5 Combine like terms: 6.726812024 + -4.5 = 2.226812024 x = 2.226812024 Simplifying x = 2.226812024Subproblem 2
x + 4.5 = -6.726812024 Simplifying x + 4.5 = -6.726812024 Reorder the terms: 4.5 + x = -6.726812024 Solving 4.5 + x = -6.726812024 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 = -6.726812024 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -6.726812024 + -4.5 x = -6.726812024 + -4.5 Combine like terms: -6.726812024 + -4.5 = -11.226812024 x = -11.226812024 Simplifying x = -11.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.226812024, -11.226812024}
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