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Simplifying x2 + -19x + 72 = 0 Reorder the terms: 72 + -19x + x2 = 0 Solving 72 + -19x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-72' to each side of the equation. 72 + -19x + -72 + x2 = 0 + -72 Reorder the terms: 72 + -72 + -19x + x2 = 0 + -72 Combine like terms: 72 + -72 = 0 0 + -19x + x2 = 0 + -72 -19x + x2 = 0 + -72 Combine like terms: 0 + -72 = -72 -19x + x2 = -72 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 = -72 + 90.25 Reorder the terms: 90.25 + -19x + x2 = -72 + 90.25 Combine like terms: -72 + 90.25 = 18.25 90.25 + -19x + x2 = 18.25 Factor a perfect square on the left side: (x + -9.5)(x + -9.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -9.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -9.5 = 4.272001873 Simplifying x + -9.5 = 4.272001873 Reorder the terms: -9.5 + x = 4.272001873 Solving -9.5 + x = 4.272001873 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 = 4.272001873 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = 4.272001873 + 9.5 x = 4.272001873 + 9.5 Combine like terms: 4.272001873 + 9.5 = 13.772001873 x = 13.772001873 Simplifying x = 13.772001873Subproblem 2
x + -9.5 = -4.272001873 Simplifying x + -9.5 = -4.272001873 Reorder the terms: -9.5 + x = -4.272001873 Solving -9.5 + x = -4.272001873 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 = -4.272001873 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + x = -4.272001873 + 9.5 x = -4.272001873 + 9.5 Combine like terms: -4.272001873 + 9.5 = 5.227998127 x = 5.227998127 Simplifying x = 5.227998127Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.772001873, 5.227998127}
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