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Simplifying x2 + 9x + -361 = 0 Reorder the terms: -361 + 9x + x2 = 0 Solving -361 + 9x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '361' to each side of the equation. -361 + 9x + 361 + x2 = 0 + 361 Reorder the terms: -361 + 361 + 9x + x2 = 0 + 361 Combine like terms: -361 + 361 = 0 0 + 9x + x2 = 0 + 361 9x + x2 = 0 + 361 Combine like terms: 0 + 361 = 361 9x + x2 = 361 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 = 361 + 20.25 Reorder the terms: 20.25 + 9x + x2 = 361 + 20.25 Combine like terms: 361 + 20.25 = 381.25 20.25 + 9x + x2 = 381.25 Factor a perfect square on the left side: (x + 4.5)(x + 4.5) = 381.25 Calculate the square root of the right side: 19.52562419 Break this problem into two subproblems by setting (x + 4.5) equal to 19.52562419 and -19.52562419.Subproblem 1
x + 4.5 = 19.52562419 Simplifying x + 4.5 = 19.52562419 Reorder the terms: 4.5 + x = 19.52562419 Solving 4.5 + x = 19.52562419 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 = 19.52562419 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = 19.52562419 + -4.5 x = 19.52562419 + -4.5 Combine like terms: 19.52562419 + -4.5 = 15.02562419 x = 15.02562419 Simplifying x = 15.02562419Subproblem 2
x + 4.5 = -19.52562419 Simplifying x + 4.5 = -19.52562419 Reorder the terms: 4.5 + x = -19.52562419 Solving 4.5 + x = -19.52562419 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 = -19.52562419 + -4.5 Combine like terms: 4.5 + -4.5 = 0.0 0.0 + x = -19.52562419 + -4.5 x = -19.52562419 + -4.5 Combine like terms: -19.52562419 + -4.5 = -24.02562419 x = -24.02562419 Simplifying x = -24.02562419Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.02562419, -24.02562419}
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