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Simplifying 4x2 + 8 + -3 = 27 + -19x Reorder the terms: 8 + -3 + 4x2 = 27 + -19x Combine like terms: 8 + -3 = 5 5 + 4x2 = 27 + -19x Solving 5 + 4x2 = 27 + -19x Solving for variable 'x'. Reorder the terms: 5 + -27 + 19x + 4x2 = 27 + -19x + -27 + 19x Combine like terms: 5 + -27 = -22 -22 + 19x + 4x2 = 27 + -19x + -27 + 19x Reorder the terms: -22 + 19x + 4x2 = 27 + -27 + -19x + 19x Combine like terms: 27 + -27 = 0 -22 + 19x + 4x2 = 0 + -19x + 19x -22 + 19x + 4x2 = -19x + 19x Combine like terms: -19x + 19x = 0 -22 + 19x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -5.5 + 4.75x + x2 = 0 Move the constant term to the right: Add '5.5' to each side of the equation. -5.5 + 4.75x + 5.5 + x2 = 0 + 5.5 Reorder the terms: -5.5 + 5.5 + 4.75x + x2 = 0 + 5.5 Combine like terms: -5.5 + 5.5 = 0.0 0.0 + 4.75x + x2 = 0 + 5.5 4.75x + x2 = 0 + 5.5 Combine like terms: 0 + 5.5 = 5.5 4.75x + x2 = 5.5 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 = 5.5 + 5.640625 Reorder the terms: 5.640625 + 4.75x + x2 = 5.5 + 5.640625 Combine like terms: 5.5 + 5.640625 = 11.140625 5.640625 + 4.75x + x2 = 11.140625 Factor a perfect square on the left side: (x + 2.375)(x + 2.375) = 11.140625 Calculate the square root of the right side: 3.337757481 Break this problem into two subproblems by setting (x + 2.375) equal to 3.337757481 and -3.337757481.Subproblem 1
x + 2.375 = 3.337757481 Simplifying x + 2.375 = 3.337757481 Reorder the terms: 2.375 + x = 3.337757481 Solving 2.375 + x = 3.337757481 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 = 3.337757481 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = 3.337757481 + -2.375 x = 3.337757481 + -2.375 Combine like terms: 3.337757481 + -2.375 = 0.962757481 x = 0.962757481 Simplifying x = 0.962757481Subproblem 2
x + 2.375 = -3.337757481 Simplifying x + 2.375 = -3.337757481 Reorder the terms: 2.375 + x = -3.337757481 Solving 2.375 + x = -3.337757481 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 = -3.337757481 + -2.375 Combine like terms: 2.375 + -2.375 = 0.000 0.000 + x = -3.337757481 + -2.375 x = -3.337757481 + -2.375 Combine like terms: -3.337757481 + -2.375 = -5.712757481 x = -5.712757481 Simplifying x = -5.712757481Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.962757481, -5.712757481}
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