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Simplifying 8x2 + -48x + 15 = 0 Reorder the terms: 15 + -48x + 8x2 = 0 Solving 15 + -48x + 8x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 8 the coefficient of the squared term: Divide each side by '8'. 1.875 + -6x + x2 = 0 Move the constant term to the right: Add '-1.875' to each side of the equation. 1.875 + -6x + -1.875 + x2 = 0 + -1.875 Reorder the terms: 1.875 + -1.875 + -6x + x2 = 0 + -1.875 Combine like terms: 1.875 + -1.875 = 0.000 0.000 + -6x + x2 = 0 + -1.875 -6x + x2 = 0 + -1.875 Combine like terms: 0 + -1.875 = -1.875 -6x + x2 = -1.875 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -1.875 + 9 Reorder the terms: 9 + -6x + x2 = -1.875 + 9 Combine like terms: -1.875 + 9 = 7.125 9 + -6x + x2 = 7.125 Factor a perfect square on the left side: (x + -3)(x + -3) = 7.125 Calculate the square root of the right side: 2.669269563 Break this problem into two subproblems by setting (x + -3) equal to 2.669269563 and -2.669269563.Subproblem 1
x + -3 = 2.669269563 Simplifying x + -3 = 2.669269563 Reorder the terms: -3 + x = 2.669269563 Solving -3 + x = 2.669269563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.669269563 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.669269563 + 3 x = 2.669269563 + 3 Combine like terms: 2.669269563 + 3 = 5.669269563 x = 5.669269563 Simplifying x = 5.669269563Subproblem 2
x + -3 = -2.669269563 Simplifying x + -3 = -2.669269563 Reorder the terms: -3 + x = -2.669269563 Solving -3 + x = -2.669269563 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.669269563 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.669269563 + 3 x = -2.669269563 + 3 Combine like terms: -2.669269563 + 3 = 0.330730437 x = 0.330730437 Simplifying x = 0.330730437Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.669269563, 0.330730437}
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