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Simplifying x2 + -89x + 1837 = 0 Reorder the terms: 1837 + -89x + x2 = 0 Solving 1837 + -89x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1837' to each side of the equation. 1837 + -89x + -1837 + x2 = 0 + -1837 Reorder the terms: 1837 + -1837 + -89x + x2 = 0 + -1837 Combine like terms: 1837 + -1837 = 0 0 + -89x + x2 = 0 + -1837 -89x + x2 = 0 + -1837 Combine like terms: 0 + -1837 = -1837 -89x + x2 = -1837 The x term is -89x. Take half its coefficient (-44.5). Square it (1980.25) and add it to both sides. Add '1980.25' to each side of the equation. -89x + 1980.25 + x2 = -1837 + 1980.25 Reorder the terms: 1980.25 + -89x + x2 = -1837 + 1980.25 Combine like terms: -1837 + 1980.25 = 143.25 1980.25 + -89x + x2 = 143.25 Factor a perfect square on the left side: (x + -44.5)(x + -44.5) = 143.25 Calculate the square root of the right side: 11.968709204 Break this problem into two subproblems by setting (x + -44.5) equal to 11.968709204 and -11.968709204.Subproblem 1
x + -44.5 = 11.968709204 Simplifying x + -44.5 = 11.968709204 Reorder the terms: -44.5 + x = 11.968709204 Solving -44.5 + x = 11.968709204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = 11.968709204 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = 11.968709204 + 44.5 x = 11.968709204 + 44.5 Combine like terms: 11.968709204 + 44.5 = 56.468709204 x = 56.468709204 Simplifying x = 56.468709204Subproblem 2
x + -44.5 = -11.968709204 Simplifying x + -44.5 = -11.968709204 Reorder the terms: -44.5 + x = -11.968709204 Solving -44.5 + x = -11.968709204 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '44.5' to each side of the equation. -44.5 + 44.5 + x = -11.968709204 + 44.5 Combine like terms: -44.5 + 44.5 = 0.0 0.0 + x = -11.968709204 + 44.5 x = -11.968709204 + 44.5 Combine like terms: -11.968709204 + 44.5 = 32.531290796 x = 32.531290796 Simplifying x = 32.531290796Solution
The solution to the problem is based on the solutions from the subproblems. x = {56.468709204, 32.531290796}
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