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Simplifying x2 + -9x = 25 Reorder the terms: -9x + x2 = 25 Solving -9x + x2 = 25 Solving for variable 'x'. Reorder the terms: -25 + -9x + x2 = 25 + -25 Combine like terms: 25 + -25 = 0 -25 + -9x + x2 = 0 Begin completing the square. 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 = 11.226812024 x = 11.226812024 Simplifying x = 11.226812024Subproblem 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 = -2.226812024 x = -2.226812024 Simplifying x = -2.226812024Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.226812024, -2.226812024}
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