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Simplifying 8x2 + -19x + -19 = 0 Reorder the terms: -19 + -19x + 8x2 = 0 Solving -19 + -19x + 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 + -2.375x + x2 = 0 Move the constant term to the right: Add '2.375' to each side of the equation. -2.375 + -2.375x + 2.375 + x2 = 0 + 2.375 Reorder the terms: -2.375 + 2.375 + -2.375x + x2 = 0 + 2.375 Combine like terms: -2.375 + 2.375 = 0.000 0.000 + -2.375x + x2 = 0 + 2.375 -2.375x + x2 = 0 + 2.375 Combine like terms: 0 + 2.375 = 2.375 -2.375x + x2 = 2.375 The x term is -2.375x. Take half its coefficient (-1.1875). Square it (1.41015625) and add it to both sides. Add '1.41015625' to each side of the equation. -2.375x + 1.41015625 + x2 = 2.375 + 1.41015625 Reorder the terms: 1.41015625 + -2.375x + x2 = 2.375 + 1.41015625 Combine like terms: 2.375 + 1.41015625 = 3.78515625 1.41015625 + -2.375x + x2 = 3.78515625 Factor a perfect square on the left side: (x + -1.1875)(x + -1.1875) = 3.78515625 Calculate the square root of the right side: 1.945547802 Break this problem into two subproblems by setting (x + -1.1875) equal to 1.945547802 and -1.945547802.Subproblem 1
x + -1.1875 = 1.945547802 Simplifying x + -1.1875 = 1.945547802 Reorder the terms: -1.1875 + x = 1.945547802 Solving -1.1875 + x = 1.945547802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = 1.945547802 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = 1.945547802 + 1.1875 x = 1.945547802 + 1.1875 Combine like terms: 1.945547802 + 1.1875 = 3.133047802 x = 3.133047802 Simplifying x = 3.133047802Subproblem 2
x + -1.1875 = -1.945547802 Simplifying x + -1.1875 = -1.945547802 Reorder the terms: -1.1875 + x = -1.945547802 Solving -1.1875 + x = -1.945547802 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.1875' to each side of the equation. -1.1875 + 1.1875 + x = -1.945547802 + 1.1875 Combine like terms: -1.1875 + 1.1875 = 0.0000 0.0000 + x = -1.945547802 + 1.1875 x = -1.945547802 + 1.1875 Combine like terms: -1.945547802 + 1.1875 = -0.758047802 x = -0.758047802 Simplifying x = -0.758047802Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.133047802, -0.758047802}
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