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Simplifying x(x + 9) = 2420 Reorder the terms: x(9 + x) = 2420 (9 * x + x * x) = 2420 (9x + x2) = 2420 Solving 9x + x2 = 2420 Solving for variable 'x'. Reorder the terms: -2420 + 9x + x2 = 2420 + -2420 Combine like terms: 2420 + -2420 = 0 -2420 + 9x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2420' to each side of the equation. -2420 + 9x + 2420 + x2 = 0 + 2420 Reorder the terms: -2420 + 2420 + 9x + x2 = 0 + 2420 Combine like terms: -2420 + 2420 = 0 0 + 9x + x2 = 0 + 2420 9x + x2 = 0 + 2420 Combine like terms: 0 + 2420 = 2420 9x + x2 = 2420 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 = 2420 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 2420 + 20.25 Combine like terms: 2420 + 20.25 = 2440.25 20.25 + 9x + x2 = 2440.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 2440.25 Calculate the square root of the right side: 49.398886627 Break this problem into two subproblems by setting (x + 4.5) equal to 49.398886627 and -49.398886627.Subproblem 1
x + 4.5 = 49.398886627 Simplifying x + 4.5 = 49.398886627 Reorder the terms: 4.5 + x = 49.398886627 Solving 4.5 + x = 49.398886627 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 = 49.398886627 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 49.398886627 + -4.5 x = 49.398886627 + -4.5 Combine like terms: 49.398886627 + -4.5 = 44.898886627 x = 44.898886627 Simplifying x = 44.898886627Subproblem 2
x + 4.5 = -49.398886627 Simplifying x + 4.5 = -49.398886627 Reorder the terms: 4.5 + x = -49.398886627 Solving 4.5 + x = -49.398886627 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 = -49.398886627 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -49.398886627 + -4.5 x = -49.398886627 + -4.5 Combine like terms: -49.398886627 + -4.5 = -53.898886627 x = -53.898886627 Simplifying x = -53.898886627Solution
The solution to the problem is based on the solutions from the subproblems. x = {44.898886627, -53.898886627}
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