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Simplifying x2 + 9x = 123 Reorder the terms: 9x + x2 = 123 Solving 9x + x2 = 123 Solving for variable 'x'. Reorder the terms: -123 + 9x + x2 = 123 + -123 Combine like terms: 123 + -123 = 0 -123 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '123' to each side of the equation. -123 + 9x + 123 + x2 = 0 + 123 Reorder the terms: -123 + 123 + 9x + x2 = 0 + 123 Combine like terms: -123 + 123 = 0 0 + 9x + x2 = 0 + 123 9x + x2 = 0 + 123 Combine like terms: 0 + 123 = 123 9x + x2 = 123 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 = 123 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 123 + 20.25 Combine like terms: 123 + 20.25 = 143.25 20.25 + 9x + x2 = 143.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 143.25 Calculate the square root of the right side: 11.968709204 Break this problem into two subproblems by setting (x + 4.5) equal to 11.968709204 and -11.968709204.Subproblem 1
x + 4.5 = 11.968709204 Simplifying x + 4.5 = 11.968709204 Reorder the terms: 4.5 + x = 11.968709204 Solving 4.5 + x = 11.968709204 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 = 11.968709204 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 11.968709204 + -4.5 x = 11.968709204 + -4.5 Combine like terms: 11.968709204 + -4.5 = 7.468709204 x = 7.468709204 Simplifying x = 7.468709204Subproblem 2
x + 4.5 = -11.968709204 Simplifying x + 4.5 = -11.968709204 Reorder the terms: 4.5 + x = -11.968709204 Solving 4.5 + x = -11.968709204 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 = -11.968709204 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -11.968709204 + -4.5 x = -11.968709204 + -4.5 Combine like terms: -11.968709204 + -4.5 = -16.468709204 x = -16.468709204 Simplifying x = -16.468709204Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.468709204, -16.468709204}
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