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Simplifying x2 + 21x + 59 = 0 Reorder the terms: 59 + 21x + x2 = 0 Solving 59 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-59' to each side of the equation. 59 + 21x + -59 + x2 = 0 + -59 Reorder the terms: 59 + -59 + 21x + x2 = 0 + -59 Combine like terms: 59 + -59 = 0 0 + 21x + x2 = 0 + -59 21x + x2 = 0 + -59 Combine like terms: 0 + -59 = -59 21x + x2 = -59 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 = -59 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -59 + 110.25 Combine like terms: -59 + 110.25 = 51.25 110.25 + 21x + x2 = 51.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 51.25 Calculate the square root of the right side: 7.158910532 Break this problem into two subproblems by setting (x + 10.5) equal to 7.158910532 and -7.158910532.Subproblem 1
x + 10.5 = 7.158910532 Simplifying x + 10.5 = 7.158910532 Reorder the terms: 10.5 + x = 7.158910532 Solving 10.5 + x = 7.158910532 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 = 7.158910532 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 7.158910532 + -10.5 x = 7.158910532 + -10.5 Combine like terms: 7.158910532 + -10.5 = -3.341089468 x = -3.341089468 Simplifying x = -3.341089468Subproblem 2
x + 10.5 = -7.158910532 Simplifying x + 10.5 = -7.158910532 Reorder the terms: 10.5 + x = -7.158910532 Solving 10.5 + x = -7.158910532 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 = -7.158910532 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -7.158910532 + -10.5 x = -7.158910532 + -10.5 Combine like terms: -7.158910532 + -10.5 = -17.658910532 x = -17.658910532 Simplifying x = -17.658910532Solution
The solution to the problem is based on the solutions from the subproblems. x = {-3.341089468, -17.658910532}
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