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Simplifying 27x2 + 37x + -10 = 0 Reorder the terms: -10 + 37x + 27x2 = 0 Solving -10 + 37x + 27x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 27 the coefficient of the squared term: Divide each side by '27'. -0.3703703704 + 1.37037037x + x2 = 0 Move the constant term to the right: Add '0.3703703704' to each side of the equation. -0.3703703704 + 1.37037037x + 0.3703703704 + x2 = 0 + 0.3703703704 Reorder the terms: -0.3703703704 + 0.3703703704 + 1.37037037x + x2 = 0 + 0.3703703704 Combine like terms: -0.3703703704 + 0.3703703704 = 0.0000000000 0.0000000000 + 1.37037037x + x2 = 0 + 0.3703703704 1.37037037x + x2 = 0 + 0.3703703704 Combine like terms: 0 + 0.3703703704 = 0.3703703704 1.37037037x + x2 = 0.3703703704 The x term is 1.37037037x. Take half its coefficient (0.685185185). Square it (0.4694787377) and add it to both sides. Add '0.4694787377' to each side of the equation. 1.37037037x + 0.4694787377 + x2 = 0.3703703704 + 0.4694787377 Reorder the terms: 0.4694787377 + 1.37037037x + x2 = 0.3703703704 + 0.4694787377 Combine like terms: 0.3703703704 + 0.4694787377 = 0.8398491081 0.4694787377 + 1.37037037x + x2 = 0.8398491081 Factor a perfect square on the left side: (x + 0.685185185)(x + 0.685185185) = 0.8398491081 Calculate the square root of the right side: 0.916432817 Break this problem into two subproblems by setting (x + 0.685185185) equal to 0.916432817 and -0.916432817.Subproblem 1
x + 0.685185185 = 0.916432817 Simplifying x + 0.685185185 = 0.916432817 Reorder the terms: 0.685185185 + x = 0.916432817 Solving 0.685185185 + x = 0.916432817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.685185185' to each side of the equation. 0.685185185 + -0.685185185 + x = 0.916432817 + -0.685185185 Combine like terms: 0.685185185 + -0.685185185 = 0.000000000 0.000000000 + x = 0.916432817 + -0.685185185 x = 0.916432817 + -0.685185185 Combine like terms: 0.916432817 + -0.685185185 = 0.231247632 x = 0.231247632 Simplifying x = 0.231247632Subproblem 2
x + 0.685185185 = -0.916432817 Simplifying x + 0.685185185 = -0.916432817 Reorder the terms: 0.685185185 + x = -0.916432817 Solving 0.685185185 + x = -0.916432817 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.685185185' to each side of the equation. 0.685185185 + -0.685185185 + x = -0.916432817 + -0.685185185 Combine like terms: 0.685185185 + -0.685185185 = 0.000000000 0.000000000 + x = -0.916432817 + -0.685185185 x = -0.916432817 + -0.685185185 Combine like terms: -0.916432817 + -0.685185185 = -1.601618002 x = -1.601618002 Simplifying x = -1.601618002Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.231247632, -1.601618002}
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