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Simplifying x2 + 21x + 7 = 0 Reorder the terms: 7 + 21x + x2 = 0 Solving 7 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-7' to each side of the equation. 7 + 21x + -7 + x2 = 0 + -7 Reorder the terms: 7 + -7 + 21x + x2 = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 21x + x2 = 0 + -7 21x + x2 = 0 + -7 Combine like terms: 0 + -7 = -7 21x + x2 = -7 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 = -7 + 110.25 Reorder the terms: 110.25 + 21x + x2 = -7 + 110.25 Combine like terms: -7 + 110.25 = 103.25 110.25 + 21x + x2 = 103.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 103.25 Calculate the square root of the right side: 10.161200716 Break this problem into two subproblems by setting (x + 10.5) equal to 10.161200716 and -10.161200716.Subproblem 1
x + 10.5 = 10.161200716 Simplifying x + 10.5 = 10.161200716 Reorder the terms: 10.5 + x = 10.161200716 Solving 10.5 + x = 10.161200716 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 = 10.161200716 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 10.161200716 + -10.5 x = 10.161200716 + -10.5 Combine like terms: 10.161200716 + -10.5 = -0.338799284 x = -0.338799284 Simplifying x = -0.338799284Subproblem 2
x + 10.5 = -10.161200716 Simplifying x + 10.5 = -10.161200716 Reorder the terms: 10.5 + x = -10.161200716 Solving 10.5 + x = -10.161200716 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 = -10.161200716 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -10.161200716 + -10.5 x = -10.161200716 + -10.5 Combine like terms: -10.161200716 + -10.5 = -20.661200716 x = -20.661200716 Simplifying x = -20.661200716Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.338799284, -20.661200716}
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