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Simplifying x2 + 43x + 77 = 0 Reorder the terms: 77 + 43x + x2 = 0 Solving 77 + 43x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-77' to each side of the equation. 77 + 43x + -77 + x2 = 0 + -77 Reorder the terms: 77 + -77 + 43x + x2 = 0 + -77 Combine like terms: 77 + -77 = 0 0 + 43x + x2 = 0 + -77 43x + x2 = 0 + -77 Combine like terms: 0 + -77 = -77 43x + x2 = -77 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 = -77 + 462.25 Reorder the terms: 462.25 + 43x + x2 = -77 + 462.25 Combine like terms: -77 + 462.25 = 385.25 462.25 + 43x + x2 = 385.25 Factor a perfect square on the left side: (x + 21.5)(x + 21.5) = 385.25 Calculate the square root of the right side: 19.627786426 Break this problem into two subproblems by setting (x + 21.5) equal to 19.627786426 and -19.627786426.Subproblem 1
x + 21.5 = 19.627786426 Simplifying x + 21.5 = 19.627786426 Reorder the terms: 21.5 + x = 19.627786426 Solving 21.5 + x = 19.627786426 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 = 19.627786426 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = 19.627786426 + -21.5 x = 19.627786426 + -21.5 Combine like terms: 19.627786426 + -21.5 = -1.872213574 x = -1.872213574 Simplifying x = -1.872213574Subproblem 2
x + 21.5 = -19.627786426 Simplifying x + 21.5 = -19.627786426 Reorder the terms: 21.5 + x = -19.627786426 Solving 21.5 + x = -19.627786426 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 = -19.627786426 + -21.5 Combine like terms: 21.5 + -21.5 = 0.0 0.0 + x = -19.627786426 + -21.5 x = -19.627786426 + -21.5 Combine like terms: -19.627786426 + -21.5 = -41.127786426 x = -41.127786426 Simplifying x = -41.127786426Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.872213574, -41.127786426}
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