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Simplifying 9x + x2 = 225 Solving 9x + x2 = 225 Solving for variable 'x'. Reorder the terms: -225 + 9x + x2 = 225 + -225 Combine like terms: 225 + -225 = 0 -225 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 9x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 9x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 9x + x2 = 0 + 225 9x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 9x + x2 = 225 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 = 225 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 225 + 20.25 Combine like terms: 225 + 20.25 = 245.25 20.25 + 9x + x2 = 245.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 245.25 Calculate the square root of the right side: 15.660459763 Break this problem into two subproblems by setting (x + 4.5) equal to 15.660459763 and -15.660459763.Subproblem 1
x + 4.5 = 15.660459763 Simplifying x + 4.5 = 15.660459763 Reorder the terms: 4.5 + x = 15.660459763 Solving 4.5 + x = 15.660459763 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 = 15.660459763 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 15.660459763 + -4.5 x = 15.660459763 + -4.5 Combine like terms: 15.660459763 + -4.5 = 11.160459763 x = 11.160459763 Simplifying x = 11.160459763Subproblem 2
x + 4.5 = -15.660459763 Simplifying x + 4.5 = -15.660459763 Reorder the terms: 4.5 + x = -15.660459763 Solving 4.5 + x = -15.660459763 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 = -15.660459763 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -15.660459763 + -4.5 x = -15.660459763 + -4.5 Combine like terms: -15.660459763 + -4.5 = -20.160459763 x = -20.160459763 Simplifying x = -20.160459763Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.160459763, -20.160459763}
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