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Simplifying x2 + 21x + 40 = 0 Reorder the terms: 40 + 21x + x2 = 0 Solving 40 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-40' to each side of the equation. 40 + 21x + -40 + x2 = 0 + -40 Reorder the terms: 40 + -40 + 21x + x2 = 0 + -40 Combine like terms: 40 + -40 = 0 0 + 21x + x2 = 0 + -40 21x + x2 = 0 + -40 Combine like terms: 0 + -40 = -40 21x + x2 = -40 The x term is 21x. Take half its coefficient (10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. 21x + 110.25 + x2 = -40 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -40 + 110.25 Combine like terms: -40 + 110.25 = 70.25 110.25 + 21x + x2 = 70.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 70.25 Calculate the square root of the right side: 8.381527307 Break this problem into two subproblems by setting (x + 10.5) equal to 8.381527307 and -8.381527307.Subproblem 1
x + 10.5 = 8.381527307 Simplifying x + 10.5 = 8.381527307 Reorder the terms: 10.5 + x = 8.381527307 Solving 10.5 + x = 8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = 8.381527307 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 8.381527307 + -10.5 x = 8.381527307 + -10.5 Combine like terms: 8.381527307 + -10.5 = -2.118472693 x = -2.118472693 Simplifying x = -2.118472693Subproblem 2
x + 10.5 = -8.381527307 Simplifying x + 10.5 = -8.381527307 Reorder the terms: 10.5 + x = -8.381527307 Solving 10.5 + x = -8.381527307 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-10.5' to each side of the equation. 10.5 + -10.5 + x = -8.381527307 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -8.381527307 + -10.5 x = -8.381527307 + -10.5 Combine like terms: -8.381527307 + -10.5 = -18.881527307 x = -18.881527307 Simplifying x = -18.881527307Solution
The solution to the problem is based on the solutions from the subproblems. x = {-2.118472693, -18.881527307}
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