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Simplifying 723x2 + 290x + -409 = 0 Reorder the terms: -409 + 290x + 723x2 = 0 Solving -409 + 290x + 723x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 723 the coefficient of the squared term: Divide each side by '723'. -0.5656984786 + 0.4011065007x + x2 = 0 Move the constant term to the right: Add '0.5656984786' to each side of the equation. -0.5656984786 + 0.4011065007x + 0.5656984786 + x2 = 0 + 0.5656984786 Reorder the terms: -0.5656984786 + 0.5656984786 + 0.4011065007x + x2 = 0 + 0.5656984786 Combine like terms: -0.5656984786 + 0.5656984786 = 0.0000000000 0.0000000000 + 0.4011065007x + x2 = 0 + 0.5656984786 0.4011065007x + x2 = 0 + 0.5656984786 Combine like terms: 0 + 0.5656984786 = 0.5656984786 0.4011065007x + x2 = 0.5656984786 The x term is 0.4011065007x. Take half its coefficient (0.2005532504). Square it (0.04022160625) and add it to both sides. Add '0.04022160625' to each side of the equation. 0.4011065007x + 0.04022160625 + x2 = 0.5656984786 + 0.04022160625 Reorder the terms: 0.04022160625 + 0.4011065007x + x2 = 0.5656984786 + 0.04022160625 Combine like terms: 0.5656984786 + 0.04022160625 = 0.60592008485 0.04022160625 + 0.4011065007x + x2 = 0.60592008485 Factor a perfect square on the left side: (x + 0.2005532504)(x + 0.2005532504) = 0.60592008485 Calculate the square root of the right side: 0.778408688 Break this problem into two subproblems by setting (x + 0.2005532504) equal to 0.778408688 and -0.778408688.Subproblem 1
x + 0.2005532504 = 0.778408688 Simplifying x + 0.2005532504 = 0.778408688 Reorder the terms: 0.2005532504 + x = 0.778408688 Solving 0.2005532504 + x = 0.778408688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2005532504' to each side of the equation. 0.2005532504 + -0.2005532504 + x = 0.778408688 + -0.2005532504 Combine like terms: 0.2005532504 + -0.2005532504 = 0.0000000000 0.0000000000 + x = 0.778408688 + -0.2005532504 x = 0.778408688 + -0.2005532504 Combine like terms: 0.778408688 + -0.2005532504 = 0.5778554376 x = 0.5778554376 Simplifying x = 0.5778554376Subproblem 2
x + 0.2005532504 = -0.778408688 Simplifying x + 0.2005532504 = -0.778408688 Reorder the terms: 0.2005532504 + x = -0.778408688 Solving 0.2005532504 + x = -0.778408688 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2005532504' to each side of the equation. 0.2005532504 + -0.2005532504 + x = -0.778408688 + -0.2005532504 Combine like terms: 0.2005532504 + -0.2005532504 = 0.0000000000 0.0000000000 + x = -0.778408688 + -0.2005532504 x = -0.778408688 + -0.2005532504 Combine like terms: -0.778408688 + -0.2005532504 = -0.9789619384 x = -0.9789619384 Simplifying x = -0.9789619384Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5778554376, -0.9789619384}
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