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Simplifying 0 = x2 + -15x + 38 Reorder the terms: 0 = 38 + -15x + x2 Solving 0 = 38 + -15x + x2 Solving for variable 'x'. Combine like terms: 0 + -38 = -38 -38 + 15x + -1x2 = 38 + -15x + x2 + -38 + 15x + -1x2 Reorder the terms: -38 + 15x + -1x2 = 38 + -38 + -15x + 15x + x2 + -1x2 Combine like terms: 38 + -38 = 0 -38 + 15x + -1x2 = 0 + -15x + 15x + x2 + -1x2 -38 + 15x + -1x2 = -15x + 15x + x2 + -1x2 Combine like terms: -15x + 15x = 0 -38 + 15x + -1x2 = 0 + x2 + -1x2 -38 + 15x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -38 + 15x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 38 + -15x + x2 = 0 Move the constant term to the right: Add '-38' to each side of the equation. 38 + -15x + -38 + x2 = 0 + -38 Reorder the terms: 38 + -38 + -15x + x2 = 0 + -38 Combine like terms: 38 + -38 = 0 0 + -15x + x2 = 0 + -38 -15x + x2 = 0 + -38 Combine like terms: 0 + -38 = -38 -15x + x2 = -38 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 = -38 + 56.25 Reorder the terms: 56.25 + -15x + x2 = -38 + 56.25 Combine like terms: -38 + 56.25 = 18.25 56.25 + -15x + x2 = 18.25 Factor a perfect square on the left side: (x + -7.5)(x + -7.5) = 18.25 Calculate the square root of the right side: 4.272001873 Break this problem into two subproblems by setting (x + -7.5) equal to 4.272001873 and -4.272001873.Subproblem 1
x + -7.5 = 4.272001873 Simplifying x + -7.5 = 4.272001873 Reorder the terms: -7.5 + x = 4.272001873 Solving -7.5 + x = 4.272001873 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 = 4.272001873 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = 4.272001873 + 7.5 x = 4.272001873 + 7.5 Combine like terms: 4.272001873 + 7.5 = 11.772001873 x = 11.772001873 Simplifying x = 11.772001873Subproblem 2
x + -7.5 = -4.272001873 Simplifying x + -7.5 = -4.272001873 Reorder the terms: -7.5 + x = -4.272001873 Solving -7.5 + x = -4.272001873 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 = -4.272001873 + 7.5 Combine like terms: -7.5 + 7.5 = 0.0 0.0 + x = -4.272001873 + 7.5 x = -4.272001873 + 7.5 Combine like terms: -4.272001873 + 7.5 = 3.227998127 x = 3.227998127 Simplifying x = 3.227998127Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.772001873, 3.227998127}
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