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Simplifying 0 = x2 + -78x + -1911 Reorder the terms: 0 = -1911 + -78x + x2 Solving 0 = -1911 + -78x + x2 Solving for variable 'x'. Combine like terms: 0 + 1911 = 1911 1911 + 78x + -1x2 = -1911 + -78x + x2 + 1911 + 78x + -1x2 Reorder the terms: 1911 + 78x + -1x2 = -1911 + 1911 + -78x + 78x + x2 + -1x2 Combine like terms: -1911 + 1911 = 0 1911 + 78x + -1x2 = 0 + -78x + 78x + x2 + -1x2 1911 + 78x + -1x2 = -78x + 78x + x2 + -1x2 Combine like terms: -78x + 78x = 0 1911 + 78x + -1x2 = 0 + x2 + -1x2 1911 + 78x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 1911 + 78x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -1911 + -78x + x2 = 0 Move the constant term to the right: Add '1911' to each side of the equation. -1911 + -78x + 1911 + x2 = 0 + 1911 Reorder the terms: -1911 + 1911 + -78x + x2 = 0 + 1911 Combine like terms: -1911 + 1911 = 0 0 + -78x + x2 = 0 + 1911 -78x + x2 = 0 + 1911 Combine like terms: 0 + 1911 = 1911 -78x + x2 = 1911 The x term is -78x. Take half its coefficient (-39). Square it (1521) and add it to both sides. Add '1521' to each side of the equation. -78x + 1521 + x2 = 1911 + 1521 Reorder the terms: 1521 + -78x + x2 = 1911 + 1521 Combine like terms: 1911 + 1521 = 3432 1521 + -78x + x2 = 3432 Factor a perfect square on the left side: (x + -39)(x + -39) = 3432 Calculate the square root of the right side: 58.583274064 Break this problem into two subproblems by setting (x + -39) equal to 58.583274064 and -58.583274064.Subproblem 1
x + -39 = 58.583274064 Simplifying x + -39 = 58.583274064 Reorder the terms: -39 + x = 58.583274064 Solving -39 + x = 58.583274064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = 58.583274064 + 39 Combine like terms: -39 + 39 = 0 0 + x = 58.583274064 + 39 x = 58.583274064 + 39 Combine like terms: 58.583274064 + 39 = 97.583274064 x = 97.583274064 Simplifying x = 97.583274064Subproblem 2
x + -39 = -58.583274064 Simplifying x + -39 = -58.583274064 Reorder the terms: -39 + x = -58.583274064 Solving -39 + x = -58.583274064 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '39' to each side of the equation. -39 + 39 + x = -58.583274064 + 39 Combine like terms: -39 + 39 = 0 0 + x = -58.583274064 + 39 x = -58.583274064 + 39 Combine like terms: -58.583274064 + 39 = -19.583274064 x = -19.583274064 Simplifying x = -19.583274064Solution
The solution to the problem is based on the solutions from the subproblems. x = {97.583274064, -19.583274064}
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