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Simplifying 6x2 + -15x + -38 = 0 Reorder the terms: -38 + -15x + 6x2 = 0 Solving -38 + -15x + 6x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -6.333333333 + -2.5x + x2 = 0 Move the constant term to the right: Add '6.333333333' to each side of the equation. -6.333333333 + -2.5x + 6.333333333 + x2 = 0 + 6.333333333 Reorder the terms: -6.333333333 + 6.333333333 + -2.5x + x2 = 0 + 6.333333333 Combine like terms: -6.333333333 + 6.333333333 = 0.000000000 0.000000000 + -2.5x + x2 = 0 + 6.333333333 -2.5x + x2 = 0 + 6.333333333 Combine like terms: 0 + 6.333333333 = 6.333333333 -2.5x + x2 = 6.333333333 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 6.333333333 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 6.333333333 + 1.5625 Combine like terms: 6.333333333 + 1.5625 = 7.895833333 1.5625 + -2.5x + x2 = 7.895833333 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 7.895833333 Calculate the square root of the right side: 2.80995255 Break this problem into two subproblems by setting (x + -1.25) equal to 2.80995255 and -2.80995255.Subproblem 1
x + -1.25 = 2.80995255 Simplifying x + -1.25 = 2.80995255 Reorder the terms: -1.25 + x = 2.80995255 Solving -1.25 + x = 2.80995255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.80995255 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.80995255 + 1.25 x = 2.80995255 + 1.25 Combine like terms: 2.80995255 + 1.25 = 4.05995255 x = 4.05995255 Simplifying x = 4.05995255Subproblem 2
x + -1.25 = -2.80995255 Simplifying x + -1.25 = -2.80995255 Reorder the terms: -1.25 + x = -2.80995255 Solving -1.25 + x = -2.80995255 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.80995255 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.80995255 + 1.25 x = -2.80995255 + 1.25 Combine like terms: -2.80995255 + 1.25 = -1.55995255 x = -1.55995255 Simplifying x = -1.55995255Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.05995255, -1.55995255}
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