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Simplifying 2.3x2 + 0.7x + -0.59 = 0 Reorder the terms: -0.59 + 0.7x + 2.3x2 = 0 Solving -0.59 + 0.7x + 2.3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2.3 the coefficient of the squared term: Divide each side by '2.3'. -0.2565217391 + 0.3043478261x + x2 = 0 Move the constant term to the right: Add '0.2565217391' to each side of the equation. -0.2565217391 + 0.3043478261x + 0.2565217391 + x2 = 0 + 0.2565217391 Reorder the terms: -0.2565217391 + 0.2565217391 + 0.3043478261x + x2 = 0 + 0.2565217391 Combine like terms: -0.2565217391 + 0.2565217391 = 0.0000000000 0.0000000000 + 0.3043478261x + x2 = 0 + 0.2565217391 0.3043478261x + x2 = 0 + 0.2565217391 Combine like terms: 0 + 0.2565217391 = 0.2565217391 0.3043478261x + x2 = 0.2565217391 The x term is 0.3043478261x. Take half its coefficient (0.1521739131). Square it (0.02315689983) and add it to both sides. Add '0.02315689983' to each side of the equation. 0.3043478261x + 0.02315689983 + x2 = 0.2565217391 + 0.02315689983 Reorder the terms: 0.02315689983 + 0.3043478261x + x2 = 0.2565217391 + 0.02315689983 Combine like terms: 0.2565217391 + 0.02315689983 = 0.27967863893 0.02315689983 + 0.3043478261x + x2 = 0.27967863893 Factor a perfect square on the left side: (x + 0.1521739131)(x + 0.1521739131) = 0.27967863893 Calculate the square root of the right side: 0.528846517 Break this problem into two subproblems by setting (x + 0.1521739131) equal to 0.528846517 and -0.528846517.Subproblem 1
x + 0.1521739131 = 0.528846517 Simplifying x + 0.1521739131 = 0.528846517 Reorder the terms: 0.1521739131 + x = 0.528846517 Solving 0.1521739131 + x = 0.528846517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1521739131' to each side of the equation. 0.1521739131 + -0.1521739131 + x = 0.528846517 + -0.1521739131 Combine like terms: 0.1521739131 + -0.1521739131 = 0.0000000000 0.0000000000 + x = 0.528846517 + -0.1521739131 x = 0.528846517 + -0.1521739131 Combine like terms: 0.528846517 + -0.1521739131 = 0.3766726039 x = 0.3766726039 Simplifying x = 0.3766726039Subproblem 2
x + 0.1521739131 = -0.528846517 Simplifying x + 0.1521739131 = -0.528846517 Reorder the terms: 0.1521739131 + x = -0.528846517 Solving 0.1521739131 + x = -0.528846517 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1521739131' to each side of the equation. 0.1521739131 + -0.1521739131 + x = -0.528846517 + -0.1521739131 Combine like terms: 0.1521739131 + -0.1521739131 = 0.0000000000 0.0000000000 + x = -0.528846517 + -0.1521739131 x = -0.528846517 + -0.1521739131 Combine like terms: -0.528846517 + -0.1521739131 = -0.6810204301 x = -0.6810204301 Simplifying x = -0.6810204301Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.3766726039, -0.6810204301}
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