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Simplifying x2 + 21x + -5 = 0 Reorder the terms: -5 + 21x + x2 = 0 Solving -5 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '5' to each side of the equation. -5 + 21x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + 21x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 21x + x2 = 0 + 5 21x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 21x + x2 = 5 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 = 5 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 5 + 110.25 Combine like terms: 5 + 110.25 = 115.25 110.25 + 21x + x2 = 115.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 115.25 Calculate the square root of the right side: 10.735455277 Break this problem into two subproblems by setting (x + 10.5) equal to 10.735455277 and -10.735455277.Subproblem 1
x + 10.5 = 10.735455277 Simplifying x + 10.5 = 10.735455277 Reorder the terms: 10.5 + x = 10.735455277 Solving 10.5 + x = 10.735455277 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 = 10.735455277 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 10.735455277 + -10.5 x = 10.735455277 + -10.5 Combine like terms: 10.735455277 + -10.5 = 0.235455277 x = 0.235455277 Simplifying x = 0.235455277Subproblem 2
x + 10.5 = -10.735455277 Simplifying x + 10.5 = -10.735455277 Reorder the terms: 10.5 + x = -10.735455277 Solving 10.5 + x = -10.735455277 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 = -10.735455277 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -10.735455277 + -10.5 x = -10.735455277 + -10.5 Combine like terms: -10.735455277 + -10.5 = -21.235455277 x = -21.235455277 Simplifying x = -21.235455277Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.235455277, -21.235455277}
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