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Simplifying x2 + 43x + -30 = 0 Reorder the terms: -30 + 43x + x2 = 0 Solving -30 + 43x + 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 + 43x + 30 + x2 = 0 + 30 Reorder the terms: -30 + 30 + 43x + x2 = 0 + 30 Combine like terms: -30 + 30 = 0 0 + 43x + x2 = 0 + 30 43x + x2 = 0 + 30 Combine like terms: 0 + 30 = 30 43x + x2 = 30 The x term is 43x. Take half its coefficient (21.5). Square it (462.25) and add it to both sides. Add '462.25' to each side of the equation. 43x + 462.25 + x2 = 30 + 462.25 Reorder the terms: 462.25 + 43x + x2 = 30 + 462.25 Combine like terms: 30 + 462.25 = 492.25 462.25 + 43x + x2 = 492.25 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 492.25 Calculate the square root of the right side: 22.186707732 Break this problem into two subproblems by setting (x + 21.5) equal to 22.186707732 and -22.186707732.Subproblem 1
x + 21.5 = 22.186707732 Simplifying x + 21.5 = 22.186707732 Reorder the terms: 21.5 + x = 22.186707732 Solving 21.5 + x = 22.186707732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = 22.186707732 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 22.186707732 + -21.5 x = 22.186707732 + -21.5 Combine like terms: 22.186707732 + -21.5 = 0.686707732 x = 0.686707732 Simplifying x = 0.686707732Subproblem 2
x + 21.5 = -22.186707732 Simplifying x + 21.5 = -22.186707732 Reorder the terms: 21.5 + x = -22.186707732 Solving 21.5 + x = -22.186707732 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-21.5' to each side of the equation. 21.5 + -21.5 + x = -22.186707732 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -22.186707732 + -21.5 x = -22.186707732 + -21.5 Combine like terms: -22.186707732 + -21.5 = -43.686707732 x = -43.686707732 Simplifying x = -43.686707732Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.686707732, -43.686707732}
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