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Simplifying 4x2 + 19x + -8 = 0 Reorder the terms: -8 + 19x + 4x2 = 0 Solving -8 + 19x + 4x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -2 + 4.75x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.75x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4.75x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.75x + x2 = 0 + 2 4.75x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.75x + x2 = 2 The x term is 4.75x. Take half its coefficient (2.375). Square it (5.640625) and add it to both sides. Add '5.640625' to each side of the equation. 4.75x + 5.640625 + x2 = 2 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 2 + 5.640625 Combine like terms: 2 + 5.640625 = 7.640625 5.640625 + 4.75x + x2 = 7.640625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 7.640625 Calculate the square root of the right side: 2.764168048 Break this problem into two subproblems by setting (x + 2.375) equal to 2.764168048 and -2.764168048.Subproblem 1
x + 2.375 = 2.764168048 Simplifying x + 2.375 = 2.764168048 Reorder the terms: 2.375 + x = 2.764168048 Solving 2.375 + x = 2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = 2.764168048 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 2.764168048 + -2.375 x = 2.764168048 + -2.375 Combine like terms: 2.764168048 + -2.375 = 0.389168048 x = 0.389168048 Simplifying x = 0.389168048Subproblem 2
x + 2.375 = -2.764168048 Simplifying x + 2.375 = -2.764168048 Reorder the terms: 2.375 + x = -2.764168048 Solving 2.375 + x = -2.764168048 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.375' to each side of the equation. 2.375 + -2.375 + x = -2.764168048 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -2.764168048 + -2.375 x = -2.764168048 + -2.375 Combine like terms: -2.764168048 + -2.375 = -5.139168048 x = -5.139168048 Simplifying x = -5.139168048Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.389168048, -5.139168048}
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