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Simplifying 0 = x2 + -19x + -299 Reorder the terms: 0 = -299 + -19x + x2 Solving 0 = -299 + -19x + x2 Solving for variable 'x'. Combine like terms: 0 + 299 = 299 299 + 19x + -1x2 = -299 + -19x + x2 + 299 + 19x + -1x2 Reorder the terms: 299 + 19x + -1x2 = -299 + 299 + -19x + 19x + x2 + -1x2 Combine like terms: -299 + 299 = 0 299 + 19x + -1x2 = 0 + -19x + 19x + x2 + -1x2 299 + 19x + -1x2 = -19x + 19x + x2 + -1x2 Combine like terms: -19x + 19x = 0 299 + 19x + -1x2 = 0 + x2 + -1x2 299 + 19x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 299 + 19x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -299 + -19x + x2 = 0 Move the constant term to the right: Add '299' to each side of the equation. -299 + -19x + 299 + x2 = 0 + 299 Reorder the terms: -299 + 299 + -19x + x2 = 0 + 299 Combine like terms: -299 + 299 = 0 0 + -19x + x2 = 0 + 299 -19x + x2 = 0 + 299 Combine like terms: 0 + 299 = 299 -19x + x2 = 299 The x term is -19x. Take half its coefficient (-9.5). Square it (90.25) and add it to both sides. Add '90.25' to each side of the equation. -19x + 90.25 + x2 = 299 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 299 + 90.25 Combine like terms: 299 + 90.25 = 389.25 90.25 + -19x + x2 = 389.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 389.25 Calculate the square root of the right side: 19.729419657 Break this problem into two subproblems by setting (x + -9.5) equal to 19.729419657 and -19.729419657.Subproblem 1
x + -9.5 = 19.729419657 Simplifying x + -9.5 = 19.729419657 Reorder the terms: -9.5 + x = 19.729419657 Solving -9.5 + x = 19.729419657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = 19.729419657 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 19.729419657 + 9.5 x = 19.729419657 + 9.5 Combine like terms: 19.729419657 + 9.5 = 29.229419657 x = 29.229419657 Simplifying x = 29.229419657Subproblem 2
x + -9.5 = -19.729419657 Simplifying x + -9.5 = -19.729419657 Reorder the terms: -9.5 + x = -19.729419657 Solving -9.5 + x = -19.729419657 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9.5' to each side of the equation. -9.5 + 9.5 + x = -19.729419657 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -19.729419657 + 9.5 x = -19.729419657 + 9.5 Combine like terms: -19.729419657 + 9.5 = -10.229419657 x = -10.229419657 Simplifying x = -10.229419657Solution
The solution to the problem is based on the solutions from the subproblems. x = {29.229419657, -10.229419657}
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