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Simplifying x2 + -21x + 92 = 0 Reorder the terms: 92 + -21x + x2 = 0 Solving 92 + -21x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-92' to each side of the equation. 92 + -21x + -92 + x2 = 0 + -92 Reorder the terms: 92 + -92 + -21x + x2 = 0 + -92 Combine like terms: 92 + -92 = 0 0 + -21x + x2 = 0 + -92 -21x + x2 = 0 + -92 Combine like terms: 0 + -92 = -92 -21x + x2 = -92 The x term is -21x. Take half its coefficient (-10.5). Square it (110.25) and add it to both sides. Add '110.25' to each side of the equation. -21x + 110.25 + x2 = -92 + 110.25 Reorder the terms: 110.25 + -21x + x2 = -92 + 110.25 Combine like terms: -92 + 110.25 = 18.25 110.25 + -21x + x2 = 18.25 Factor a perfect square on the left side: (x + -10.5)(x + -10.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -10.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -10.5 = 4.272001873 Simplifying x + -10.5 = 4.272001873 Reorder the terms: -10.5 + x = 4.272001873 Solving -10.5 + x = 4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = 4.272001873 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = 4.272001873 + 10.5 x = 4.272001873 + 10.5 Combine like terms: 4.272001873 + 10.5 = 14.772001873 x = 14.772001873 Simplifying x = 14.772001873Subproblem 2
x + -10.5 = -4.272001873 Simplifying x + -10.5 = -4.272001873 Reorder the terms: -10.5 + x = -4.272001873 Solving -10.5 + x = -4.272001873 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10.5' to each side of the equation. -10.5 + 10.5 + x = -4.272001873 + 10.5 Combine like terms: -10.5 + 10.5 = 0.0 0.0 + x = -4.272001873 + 10.5 x = -4.272001873 + 10.5 Combine like terms: -4.272001873 + 10.5 = 6.227998127 x = 6.227998127 Simplifying x = 6.227998127Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.772001873, 6.227998127}
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