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Simplifying x2 + 41x + -390 = 0 Reorder the terms: -390 + 41x + x2 = 0 Solving -390 + 41x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '390' to each side of the equation. -390 + 41x + 390 + x2 = 0 + 390 Reorder the terms: -390 + 390 + 41x + x2 = 0 + 390 Combine like terms: -390 + 390 = 0 0 + 41x + x2 = 0 + 390 41x + x2 = 0 + 390 Combine like terms: 0 + 390 = 390 41x + x2 = 390 The x term is 41x. Take half its coefficient (20.5). Square it (420.25) and add it to both sides. Add '420.25' to each side of the equation. 41x + 420.25 + x2 = 390 + 420.25 Reorder the terms: 420.25 + 41x + x2 = 390 + 420.25 Combine like terms: 390 + 420.25 = 810.25 420.25 + 41x + x2 = 810.25 Factor a perfect square on the left side: (x + 20.5)(x + 20.5) = 810.25 Calculate the square root of the right side: 28.464890655 Break this problem into two subproblems by setting (x + 20.5) equal to 28.464890655 and -28.464890655.Subproblem 1
x + 20.5 = 28.464890655 Simplifying x + 20.5 = 28.464890655 Reorder the terms: 20.5 + x = 28.464890655 Solving 20.5 + x = 28.464890655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = 28.464890655 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = 28.464890655 + -20.5 x = 28.464890655 + -20.5 Combine like terms: 28.464890655 + -20.5 = 7.964890655 x = 7.964890655 Simplifying x = 7.964890655Subproblem 2
x + 20.5 = -28.464890655 Simplifying x + 20.5 = -28.464890655 Reorder the terms: 20.5 + x = -28.464890655 Solving 20.5 + x = -28.464890655 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-20.5' to each side of the equation. 20.5 + -20.5 + x = -28.464890655 + -20.5 Combine like terms: 20.5 + -20.5 = 0.0 0.0 + x = -28.464890655 + -20.5 x = -28.464890655 + -20.5 Combine like terms: -28.464890655 + -20.5 = -48.964890655 x = -48.964890655 Simplifying x = -48.964890655Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.964890655, -48.964890655}
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