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Simplifying x2 + 21x + -30 = 0 Reorder the terms: -30 + 21x + x2 = 0 Solving -30 + 21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '30' to each side of the equation. -30 + 21x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 21x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 21x + x2 = 0 + 30 21x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 21x + x2 = 30 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 = 30 + 110.25 Reorder the terms: 110.25 + 21x + x2 = 30 + 110.25 Combine like terms: 30 + 110.25 = 140.25 110.25 + 21x + x2 = 140.25 Factor a perfect square on the left side: (x + 10.5)(x + 10.5) = 140.25 Calculate the square root of the right side: 11.842719282 Break this problem into two subproblems by setting (x + 10.5) equal to 11.842719282 and -11.842719282.Subproblem 1
x + 10.5 = 11.842719282 Simplifying x + 10.5 = 11.842719282 Reorder the terms: 10.5 + x = 11.842719282 Solving 10.5 + x = 11.842719282 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 = 11.842719282 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = 11.842719282 + -10.5 x = 11.842719282 + -10.5 Combine like terms: 11.842719282 + -10.5 = 1.342719282 x = 1.342719282 Simplifying x = 1.342719282Subproblem 2
x + 10.5 = -11.842719282 Simplifying x + 10.5 = -11.842719282 Reorder the terms: 10.5 + x = -11.842719282 Solving 10.5 + x = -11.842719282 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 = -11.842719282 + -10.5 Combine like terms: 10.5 + -10.5 = 0.0 0.0 + x = -11.842719282 + -10.5 x = -11.842719282 + -10.5 Combine like terms: -11.842719282 + -10.5 = -22.342719282 x = -22.342719282 Simplifying x = -22.342719282Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.342719282, -22.342719282}
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