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Simplifying 0 = -1x2 + 5x + 22 Reorder the terms: 0 = 22 + 5x + -1x2 Solving 0 = 22 + 5x + -1x2 Solving for variable 'x'. Combine like terms: 0 + -22 = -22 -22 + -5x + x2 = 22 + 5x + -1x2 + -22 + -5x + x2 Reorder the terms: -22 + -5x + x2 = 22 + -22 + 5x + -5x + -1x2 + x2 Combine like terms: 22 + -22 = 0 -22 + -5x + x2 = 0 + 5x + -5x + -1x2 + x2 -22 + -5x + x2 = 5x + -5x + -1x2 + x2 Combine like terms: 5x + -5x = 0 -22 + -5x + x2 = 0 + -1x2 + x2 -22 + -5x + x2 = -1x2 + x2 Combine like terms: -1x2 + x2 = 0 -22 + -5x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '22' to each side of the equation. -22 + -5x + 22 + x2 = 0 + 22 Reorder the terms: -22 + 22 + -5x + x2 = 0 + 22 Combine like terms: -22 + 22 = 0 0 + -5x + x2 = 0 + 22 -5x + x2 = 0 + 22 Combine like terms: 0 + 22 = 22 -5x + x2 = 22 The x term is -5x. Take half its coefficient (-2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. -5x + 6.25 + x2 = 22 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 22 + 6.25 Combine like terms: 22 + 6.25 = 28.25 6.25 + -5x + x2 = 28.25 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -2.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -2.5 = 5.315072906 Simplifying x + -2.5 = 5.315072906 Reorder the terms: -2.5 + x = 5.315072906 Solving -2.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = 5.315072906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 5.315072906 + 2.5 x = 5.315072906 + 2.5 Combine like terms: 5.315072906 + 2.5 = 7.815072906 x = 7.815072906 Simplifying x = 7.815072906Subproblem 2
x + -2.5 = -5.315072906 Simplifying x + -2.5 = -5.315072906 Reorder the terms: -2.5 + x = -5.315072906 Solving -2.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.5' to each side of the equation. -2.5 + 2.5 + x = -5.315072906 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -5.315072906 + 2.5 x = -5.315072906 + 2.5 Combine like terms: -5.315072906 + 2.5 = -2.815072906 x = -2.815072906 Simplifying x = -2.815072906Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.815072906, -2.815072906}
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