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Simplifying x2 + 5x + -243 = 0 Reorder the terms: -243 + 5x + x2 = 0 Solving -243 + 5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '243' to each side of the equation. -243 + 5x + 243 + x2 = 0 + 243 Reorder the terms: -243 + 243 + 5x + x2 = 0 + 243 Combine like terms: -243 + 243 = 0 0 + 5x + x2 = 0 + 243 5x + x2 = 0 + 243 Combine like terms: 0 + 243 = 243 5x + x2 = 243 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 243 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 243 + 6.25 Combine like terms: 243 + 6.25 = 249.25 6.25 + 5x + x2 = 249.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 249.25 Calculate the square root of the right side: 15.787653404 Break this problem into two subproblems by setting (x + 2.5) equal to 15.787653404 and -15.787653404.Subproblem 1
x + 2.5 = 15.787653404 Simplifying x + 2.5 = 15.787653404 Reorder the terms: 2.5 + x = 15.787653404 Solving 2.5 + x = 15.787653404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 15.787653404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 15.787653404 + -2.5 x = 15.787653404 + -2.5 Combine like terms: 15.787653404 + -2.5 = 13.287653404 x = 13.287653404 Simplifying x = 13.287653404Subproblem 2
x + 2.5 = -15.787653404 Simplifying x + 2.5 = -15.787653404 Reorder the terms: 2.5 + x = -15.787653404 Solving 2.5 + x = -15.787653404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -15.787653404 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -15.787653404 + -2.5 x = -15.787653404 + -2.5 Combine like terms: -15.787653404 + -2.5 = -18.287653404 x = -18.287653404 Simplifying x = -18.287653404Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.287653404, -18.287653404}
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