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Simplifying 5.5x + x2 = 23.4375 Solving 5.5x + x2 = 23.4375 Solving for variable 'x'. Reorder the terms: -23.4375 + 5.5x + x2 = 23.4375 + -23.4375 Combine like terms: 23.4375 + -23.4375 = 0.0000 -23.4375 + 5.5x + x2 = 0.0000 Begin completing the square. Move the constant term to the right: Add '23.4375' to each side of the equation. -23.4375 + 5.5x + 23.4375 + x2 = 0.0000 + 23.4375 Reorder the terms: -23.4375 + 23.4375 + 5.5x + x2 = 0.0000 + 23.4375 Combine like terms: -23.4375 + 23.4375 = 0.0000 0.0000 + 5.5x + x2 = 0.0000 + 23.4375 5.5x + x2 = 0.0000 + 23.4375 Combine like terms: 0.0000 + 23.4375 = 23.4375 5.5x + x2 = 23.4375 The x term is 5.5x. Take half its coefficient (2.75). Square it (7.5625) and add it to both sides. Add '7.5625' to each side of the equation. 5.5x + 7.5625 + x2 = 23.4375 + 7.5625 Reorder the terms: 7.5625 + 5.5x + x2 = 23.4375 + 7.5625 Combine like terms: 23.4375 + 7.5625 = 31 7.5625 + 5.5x + x2 = 31 Factor a perfect square on the left side: (x + 2.75)(x + 2.75) = 31 Calculate the square root of the right side: 5.567764363 Break this problem into two subproblems by setting (x + 2.75) equal to 5.567764363 and -5.567764363.Subproblem 1
x + 2.75 = 5.567764363 Simplifying x + 2.75 = 5.567764363 Reorder the terms: 2.75 + x = 5.567764363 Solving 2.75 + x = 5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = 5.567764363 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = 5.567764363 + -2.75 x = 5.567764363 + -2.75 Combine like terms: 5.567764363 + -2.75 = 2.817764363 x = 2.817764363 Simplifying x = 2.817764363Subproblem 2
x + 2.75 = -5.567764363 Simplifying x + 2.75 = -5.567764363 Reorder the terms: 2.75 + x = -5.567764363 Solving 2.75 + x = -5.567764363 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.75' to each side of the equation. 2.75 + -2.75 + x = -5.567764363 + -2.75 Combine like terms: 2.75 + -2.75 = 0.00 0.00 + x = -5.567764363 + -2.75 x = -5.567764363 + -2.75 Combine like terms: -5.567764363 + -2.75 = -8.317764363 x = -8.317764363 Simplifying x = -8.317764363Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.817764363, -8.317764363}
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