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Simplifying 8x2 + -28x + -19 = 0 Reorder the terms: -19 + -28x + 8x2 = 0 Solving -19 + -28x + 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 + -3.5x + x2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -3.5x + 2.375 + x2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -3.5x + x2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -3.5x + x2 = 0 + 2.375 -3.5x + x2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -3.5x + x2 = 2.375 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 2.375 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 2.375 + 3.0625 Combine like terms: 2.375 + 3.0625 = 5.4375 3.0625 + -3.5x + x2 = 5.4375 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 5.4375 Calculate the square root of the right side: 2.331844763 Break this problem into two subproblems by setting (x + -1.75) equal to 2.331844763 and -2.331844763.Subproblem 1
x + -1.75 = 2.331844763 Simplifying x + -1.75 = 2.331844763 Reorder the terms: -1.75 + x = 2.331844763 Solving -1.75 + x = 2.331844763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 2.331844763 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 2.331844763 + 1.75 x = 2.331844763 + 1.75 Combine like terms: 2.331844763 + 1.75 = 4.081844763 x = 4.081844763 Simplifying x = 4.081844763Subproblem 2
x + -1.75 = -2.331844763 Simplifying x + -1.75 = -2.331844763 Reorder the terms: -1.75 + x = -2.331844763 Solving -1.75 + x = -2.331844763 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -2.331844763 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -2.331844763 + 1.75 x = -2.331844763 + 1.75 Combine like terms: -2.331844763 + 1.75 = -0.581844763 x = -0.581844763 Simplifying x = -0.581844763Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.081844763, -0.581844763}
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