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Simplifying 2x2 + 35x + 27 = 0 Reorder the terms: 27 + 35x + 2x2 = 0 Solving 27 + 35x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 13.5 + 17.5x + x2 = 0 Move the constant term to the right: Add '-13.5' to each side of the equation. 13.5 + 17.5x + -13.5 + x2 = 0 + -13.5 Reorder the terms: 13.5 + -13.5 + 17.5x + x2 = 0 + -13.5 Combine like terms: 13.5 + -13.5 = 0.0 0.0 + 17.5x + x2 = 0 + -13.5 17.5x + x2 = 0 + -13.5 Combine like terms: 0 + -13.5 = -13.5 17.5x + x2 = -13.5 The x term is 17.5x. Take half its coefficient (8.75). Square it (76.5625) and add it to both sides. Add '76.5625' to each side of the equation. 17.5x + 76.5625 + x2 = -13.5 + 76.5625 Reorder the terms: 76.5625 + 17.5x + x2 = -13.5 + 76.5625 Combine like terms: -13.5 + 76.5625 = 63.0625 76.5625 + 17.5x + x2 = 63.0625 Factor a perfect square on the left side: (x + 8.75)(x + 8.75) = 63.0625 Calculate the square root of the right side: 7.941190087 Break this problem into two subproblems by setting (x + 8.75) equal to 7.941190087 and -7.941190087.Subproblem 1
x + 8.75 = 7.941190087 Simplifying x + 8.75 = 7.941190087 Reorder the terms: 8.75 + x = 7.941190087 Solving 8.75 + x = 7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = 7.941190087 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = 7.941190087 + -8.75 x = 7.941190087 + -8.75 Combine like terms: 7.941190087 + -8.75 = -0.808809913 x = -0.808809913 Simplifying x = -0.808809913Subproblem 2
x + 8.75 = -7.941190087 Simplifying x + 8.75 = -7.941190087 Reorder the terms: 8.75 + x = -7.941190087 Solving 8.75 + x = -7.941190087 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-8.75' to each side of the equation. 8.75 + -8.75 + x = -7.941190087 + -8.75 Combine like terms: 8.75 + -8.75 = 0.00 0.00 + x = -7.941190087 + -8.75 x = -7.941190087 + -8.75 Combine like terms: -7.941190087 + -8.75 = -16.691190087 x = -16.691190087 Simplifying x = -16.691190087Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.808809913, -16.691190087}
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