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Simplifying x2 + 43x + -60 = 0 Reorder the terms: -60 + 43x + x2 = 0 Solving -60 + 43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '60' to each side of the equation. -60 + 43x + 60 + x2 = 0 + 60 Reorder the terms: -60 + 60 + 43x + x2 = 0 + 60 Combine like terms: -60 + 60 = 0 0 + 43x + x2 = 0 + 60 43x + x2 = 0 + 60 Combine like terms: 0 + 60 = 60 43x + x2 = 60 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 = 60 + 462.25 Reorder the terms: 462.25 + 43x + x2 = 60 + 462.25 Combine like terms: 60 + 462.25 = 522.25 462.25 + 43x + x2 = 522.25 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 522.25 Calculate the square root of the right side: 22.852789764 Break this problem into two subproblems by setting (x + 21.5) equal to 22.852789764 and -22.852789764.Subproblem 1
x + 21.5 = 22.852789764 Simplifying x + 21.5 = 22.852789764 Reorder the terms: 21.5 + x = 22.852789764 Solving 21.5 + x = 22.852789764 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 = 22.852789764 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 22.852789764 + -21.5 x = 22.852789764 + -21.5 Combine like terms: 22.852789764 + -21.5 = 1.352789764 x = 1.352789764 Simplifying x = 1.352789764Subproblem 2
x + 21.5 = -22.852789764 Simplifying x + 21.5 = -22.852789764 Reorder the terms: 21.5 + x = -22.852789764 Solving 21.5 + x = -22.852789764 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 = -22.852789764 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -22.852789764 + -21.5 x = -22.852789764 + -21.5 Combine like terms: -22.852789764 + -21.5 = -44.352789764 x = -44.352789764 Simplifying x = -44.352789764Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.352789764, -44.352789764}
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