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Simplifying x2 + -19x + 8 = 57 Reorder the terms: 8 + -19x + x2 = 57 Solving 8 + -19x + x2 = 57 Solving for variable 'x'. Reorder the terms: 8 + -57 + -19x + x2 = 57 + -57 Combine like terms: 8 + -57 = -49 -49 + -19x + x2 = 57 + -57 Combine like terms: 57 + -57 = 0 -49 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + -19x + 49 + x2 = 0 + 49 Reorder the terms: -49 + 49 + -19x + x2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + -19x + x2 = 0 + 49 -19x + x2 = 0 + 49 Combine like terms: 0 + 49 = 49 -19x + x2 = 49 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 = 49 + 90.25 Reorder the terms: 90.25 + -19x + x2 = 49 + 90.25 Combine like terms: 49 + 90.25 = 139.25 90.25 + -19x + x2 = 139.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 139.25 Calculate the square root of the right side: 11.800423721 Break this problem into two subproblems by setting (x + -9.5) equal to 11.800423721 and -11.800423721.Subproblem 1
x + -9.5 = 11.800423721 Simplifying x + -9.5 = 11.800423721 Reorder the terms: -9.5 + x = 11.800423721 Solving -9.5 + x = 11.800423721 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 = 11.800423721 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 11.800423721 + 9.5 x = 11.800423721 + 9.5 Combine like terms: 11.800423721 + 9.5 = 21.300423721 x = 21.300423721 Simplifying x = 21.300423721Subproblem 2
x + -9.5 = -11.800423721 Simplifying x + -9.5 = -11.800423721 Reorder the terms: -9.5 + x = -11.800423721 Solving -9.5 + x = -11.800423721 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 = -11.800423721 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -11.800423721 + 9.5 x = -11.800423721 + 9.5 Combine like terms: -11.800423721 + 9.5 = -2.300423721 x = -2.300423721 Simplifying x = -2.300423721Solution
The solution to the problem is based on the solutions from the subproblems. x = {21.300423721, -2.300423721}
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