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Simplifying x2 + -19x + 80 = 18 Reorder the terms: 80 + -19x + x2 = 18 Solving 80 + -19x + x2 = 18 Solving for variable 'x'. Reorder the terms: 80 + -18 + -19x + x2 = 18 + -18 Combine like terms: 80 + -18 = 62 62 + -19x + x2 = 18 + -18 Combine like terms: 18 + -18 = 0 62 + -19x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-62' to each side of the equation. 62 + -19x + -62 + x2 = 0 + -62 Reorder the terms: 62 + -62 + -19x + x2 = 0 + -62 Combine like terms: 62 + -62 = 0 0 + -19x + x2 = 0 + -62 -19x + x2 = 0 + -62 Combine like terms: 0 + -62 = -62 -19x + x2 = -62 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 = -62 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -62 + 90.25 Combine like terms: -62 + 90.25 = 28.25 90.25 + -19x + x2 = 28.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -9.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -9.5 = 5.315072906 Simplifying x + -9.5 = 5.315072906 Reorder the terms: -9.5 + x = 5.315072906 Solving -9.5 + x = 5.315072906 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 = 5.315072906 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 5.315072906 + 9.5 x = 5.315072906 + 9.5 Combine like terms: 5.315072906 + 9.5 = 14.815072906 x = 14.815072906 Simplifying x = 14.815072906Subproblem 2
x + -9.5 = -5.315072906 Simplifying x + -9.5 = -5.315072906 Reorder the terms: -9.5 + x = -5.315072906 Solving -9.5 + x = -5.315072906 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 = -5.315072906 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -5.315072906 + 9.5 x = -5.315072906 + 9.5 Combine like terms: -5.315072906 + 9.5 = 4.184927094 x = 4.184927094 Simplifying x = 4.184927094Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.815072906, 4.184927094}
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