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Simplifying -1x2 + 37x + -20 = 0 Reorder the terms: -20 + 37x + -1x2 = 0 Solving -20 + 37x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 20 + -37x + x2 = 0 Move the constant term to the right: Add '-20' to each side of the equation. 20 + -37x + -20 + x2 = 0 + -20 Reorder the terms: 20 + -20 + -37x + x2 = 0 + -20 Combine like terms: 20 + -20 = 0 0 + -37x + x2 = 0 + -20 -37x + x2 = 0 + -20 Combine like terms: 0 + -20 = -20 -37x + x2 = -20 The x term is -37x. Take half its coefficient (-18.5). Square it (342.25) and add it to both sides. Add '342.25' to each side of the equation. -37x + 342.25 + x2 = -20 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -20 + 342.25 Combine like terms: -20 + 342.25 = 322.25 342.25 + -37x + x2 = 322.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 322.25 Calculate the square root of the right side: 17.951323071 Break this problem into two subproblems by setting (x + -18.5) equal to 17.951323071 and -17.951323071.Subproblem 1
x + -18.5 = 17.951323071 Simplifying x + -18.5 = 17.951323071 Reorder the terms: -18.5 + x = 17.951323071 Solving -18.5 + x = 17.951323071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = 17.951323071 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 17.951323071 + 18.5 x = 17.951323071 + 18.5 Combine like terms: 17.951323071 + 18.5 = 36.451323071 x = 36.451323071 Simplifying x = 36.451323071Subproblem 2
x + -18.5 = -17.951323071 Simplifying x + -18.5 = -17.951323071 Reorder the terms: -18.5 + x = -17.951323071 Solving -18.5 + x = -17.951323071 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '18.5' to each side of the equation. -18.5 + 18.5 + x = -17.951323071 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -17.951323071 + 18.5 x = -17.951323071 + 18.5 Combine like terms: -17.951323071 + 18.5 = 0.548676929 x = 0.548676929 Simplifying x = 0.548676929Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.451323071, 0.548676929}
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