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Simplifying x2 + 21x + 89 = 0 Reorder the terms: 89 + 21x + x2 = 0 Solving 89 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-89' to each side of the equation. 89 + 21x + -89 + x2 = 0 + -89 Reorder the terms: 89 + -89 + 21x + x2 = 0 + -89 Combine like terms: 89 + -89 = 0 0 + 21x + x2 = 0 + -89 21x + x2 = 0 + -89 Combine like terms: 0 + -89 = -89 21x + x2 = -89 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 = -89 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -89 + 110.25 Combine like terms: -89 + 110.25 = 21.25 110.25 + 21x + x2 = 21.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 21.25 Calculate the square root of the right side: 4.609772229 Break this problem into two subproblems by setting (x + 10.5) equal to 4.609772229 and -4.609772229.Subproblem 1
x + 10.5 = 4.609772229 Simplifying x + 10.5 = 4.609772229 Reorder the terms: 10.5 + x = 4.609772229 Solving 10.5 + x = 4.609772229 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 = 4.609772229 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 4.609772229 + -10.5 x = 4.609772229 + -10.5 Combine like terms: 4.609772229 + -10.5 = -5.890227771 x = -5.890227771 Simplifying x = -5.890227771Subproblem 2
x + 10.5 = -4.609772229 Simplifying x + 10.5 = -4.609772229 Reorder the terms: 10.5 + x = -4.609772229 Solving 10.5 + x = -4.609772229 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 = -4.609772229 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -4.609772229 + -10.5 x = -4.609772229 + -10.5 Combine like terms: -4.609772229 + -10.5 = -15.109772229 x = -15.109772229 Simplifying x = -15.109772229Solution
The solution to the problem is based on the solutions from the subproblems. x = {-5.890227771, -15.109772229}
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