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Simplifying 8x2 + 46x + -19 = 0 Reorder the terms: -19 + 46x + 8x2 = 0 Solving -19 + 46x + 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'. -2.375 + 5.75x + x2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + 5.75x + 2.375 + x2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + 5.75x + x2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + 5.75x + x2 = 0 + 2.375 5.75x + x2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 5.75x + x2 = 2.375 The x term is 5.75x. Take half its coefficient (2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. 5.75x + 8.265625 + x2 = 2.375 + 8.265625 Reorder the terms: 8.265625 + 5.75x + x2 = 2.375 + 8.265625 Combine like terms: 2.375 + 8.265625 = 10.640625 8.265625 + 5.75x + x2 = 10.640625 Factor a perfect square on the left side: (x + 2.875)(x + 2.875) = 10.640625 Calculate the square root of the right side: 3.261997088 Break this problem into two subproblems by setting (x + 2.875) equal to 3.261997088 and -3.261997088.Subproblem 1
x + 2.875 = 3.261997088 Simplifying x + 2.875 = 3.261997088 Reorder the terms: 2.875 + x = 3.261997088 Solving 2.875 + x = 3.261997088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = 3.261997088 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = 3.261997088 + -2.875 x = 3.261997088 + -2.875 Combine like terms: 3.261997088 + -2.875 = 0.386997088 x = 0.386997088 Simplifying x = 0.386997088Subproblem 2
x + 2.875 = -3.261997088 Simplifying x + 2.875 = -3.261997088 Reorder the terms: 2.875 + x = -3.261997088 Solving 2.875 + x = -3.261997088 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.875' to each side of the equation. 2.875 + -2.875 + x = -3.261997088 + -2.875 Combine like terms: 2.875 + -2.875 = 0.000 0.000 + x = -3.261997088 + -2.875 x = -3.261997088 + -2.875 Combine like terms: -3.261997088 + -2.875 = -6.136997088 x = -6.136997088 Simplifying x = -6.136997088Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.386997088, -6.136997088}
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