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Simplifying x2 + -15x + 28 = 0 Reorder the terms: 28 + -15x + x2 = 0 Solving 28 + -15x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-28' to each side of the equation. 28 + -15x + -28 + x2 = 0 + -28 Reorder the terms: 28 + -28 + -15x + x2 = 0 + -28 Combine like terms: 28 + -28 = 0 0 + -15x + x2 = 0 + -28 -15x + x2 = 0 + -28 Combine like terms: 0 + -28 = -28 -15x + x2 = -28 The x term is -15x. Take half its coefficient (-7.5). Square it (56.25) and add it to both sides. Add '56.25' to each side of the equation. -15x + 56.25 + x2 = -28 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -28 + 56.25 Combine like terms: -28 + 56.25 = 28.25 56.25 + -15x + x2 = 28.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 28.25 Calculate the square root of the right side: 5.315072906 Break this problem into two subproblems by setting (x + -7.5) equal to 5.315072906 and -5.315072906.Subproblem 1
x + -7.5 = 5.315072906 Simplifying x + -7.5 = 5.315072906 Reorder the terms: -7.5 + x = 5.315072906 Solving -7.5 + x = 5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = 5.315072906 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 5.315072906 + 7.5 x = 5.315072906 + 7.5 Combine like terms: 5.315072906 + 7.5 = 12.815072906 x = 12.815072906 Simplifying x = 12.815072906Subproblem 2
x + -7.5 = -5.315072906 Simplifying x + -7.5 = -5.315072906 Reorder the terms: -7.5 + x = -5.315072906 Solving -7.5 + x = -5.315072906 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '7.5' to each side of the equation. -7.5 + 7.5 + x = -5.315072906 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -5.315072906 + 7.5 x = -5.315072906 + 7.5 Combine like terms: -5.315072906 + 7.5 = 2.184927094 x = 2.184927094 Simplifying x = 2.184927094Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.815072906, 2.184927094}
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