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Simplifying x2 + -37x + 34 = 0 Reorder the terms: 34 + -37x + x2 = 0 Solving 34 + -37x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-34' to each side of the equation. 34 + -37x + -34 + x2 = 0 + -34 Reorder the terms: 34 + -34 + -37x + x2 = 0 + -34 Combine like terms: 34 + -34 = 0 0 + -37x + x2 = 0 + -34 -37x + x2 = 0 + -34 Combine like terms: 0 + -34 = -34 -37x + x2 = -34 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 = -34 + 342.25 Reorder the terms: 342.25 + -37x + x2 = -34 + 342.25 Combine like terms: -34 + 342.25 = 308.25 342.25 + -37x + x2 = 308.25 Factor a perfect square on the left side: (x + -18.5)(x + -18.5) = 308.25 Calculate the square root of the right side: 17.557049866 Break this problem into two subproblems by setting (x + -18.5) equal to 17.557049866 and -17.557049866.Subproblem 1
x + -18.5 = 17.557049866 Simplifying x + -18.5 = 17.557049866 Reorder the terms: -18.5 + x = 17.557049866 Solving -18.5 + x = 17.557049866 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 = 17.557049866 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = 17.557049866 + 18.5 x = 17.557049866 + 18.5 Combine like terms: 17.557049866 + 18.5 = 36.057049866 x = 36.057049866 Simplifying x = 36.057049866Subproblem 2
x + -18.5 = -17.557049866 Simplifying x + -18.5 = -17.557049866 Reorder the terms: -18.5 + x = -17.557049866 Solving -18.5 + x = -17.557049866 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 = -17.557049866 + 18.5 Combine like terms: -18.5 + 18.5 = 0.0 0.0 + x = -17.557049866 + 18.5 x = -17.557049866 + 18.5 Combine like terms: -17.557049866 + 18.5 = 0.942950134 x = 0.942950134 Simplifying x = 0.942950134Solution
The solution to the problem is based on the solutions from the subproblems. x = {36.057049866, 0.942950134}
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