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Simplifying -1x2 + -38x + 213 = 0 Reorder the terms: 213 + -38x + -1x2 = 0 Solving 213 + -38x + -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'. -213 + 38x + x2 = 0 Move the constant term to the right: Add '213' to each side of the equation. -213 + 38x + 213 + x2 = 0 + 213 Reorder the terms: -213 + 213 + 38x + x2 = 0 + 213 Combine like terms: -213 + 213 = 0 0 + 38x + x2 = 0 + 213 38x + x2 = 0 + 213 Combine like terms: 0 + 213 = 213 38x + x2 = 213 The x term is 38x. Take half its coefficient (19). Square it (361) and add it to both sides. Add '361' to each side of the equation. 38x + 361 + x2 = 213 + 361 Reorder the terms: 361 + 38x + x2 = 213 + 361 Combine like terms: 213 + 361 = 574 361 + 38x + x2 = 574 Factor a perfect square on the left side: (x + 19)(x + 19) = 574 Calculate the square root of the right side: 23.958297101 Break this problem into two subproblems by setting (x + 19) equal to 23.958297101 and -23.958297101.Subproblem 1
x + 19 = 23.958297101 Simplifying x + 19 = 23.958297101 Reorder the terms: 19 + x = 23.958297101 Solving 19 + x = 23.958297101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = 23.958297101 + -19 Combine like terms: 19 + -19 = 0 0 + x = 23.958297101 + -19 x = 23.958297101 + -19 Combine like terms: 23.958297101 + -19 = 4.958297101 x = 4.958297101 Simplifying x = 4.958297101Subproblem 2
x + 19 = -23.958297101 Simplifying x + 19 = -23.958297101 Reorder the terms: 19 + x = -23.958297101 Solving 19 + x = -23.958297101 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-19' to each side of the equation. 19 + -19 + x = -23.958297101 + -19 Combine like terms: 19 + -19 = 0 0 + x = -23.958297101 + -19 x = -23.958297101 + -19 Combine like terms: -23.958297101 + -19 = -42.958297101 x = -42.958297101 Simplifying x = -42.958297101Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.958297101, -42.958297101}
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