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Simplifying x2 + 531.328x + -189929.6 = 0 Reorder the terms: -189929.6 + 531.328x + x2 = 0 Solving -189929.6 + 531.328x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '189929.6' to each side of the equation. -189929.6 + 531.328x + 189929.6 + x2 = 0 + 189929.6 Reorder the terms: -189929.6 + 189929.6 + 531.328x + x2 = 0 + 189929.6 Combine like terms: -189929.6 + 189929.6 = 0.0 0.0 + 531.328x + x2 = 0 + 189929.6 531.328x + x2 = 0 + 189929.6 Combine like terms: 0 + 189929.6 = 189929.6 531.328x + x2 = 189929.6 The x term is 531.328x. Take half its coefficient (265.664). Square it (70577.36090) and add it to both sides. Add '70577.36090' to each side of the equation. 531.328x + 70577.36090 + x2 = 189929.6 + 70577.36090 Reorder the terms: 70577.36090 + 531.328x + x2 = 189929.6 + 70577.36090 Combine like terms: 189929.6 + 70577.36090 = 260506.9609 70577.36090 + 531.328x + x2 = 260506.9609 Factor a perfect square on the left side: (x + 265.664)(x + 265.664) = 260506.9609 Calculate the square root of the right side: 510.398825332 Break this problem into two subproblems by setting (x + 265.664) equal to 510.398825332 and -510.398825332.Subproblem 1
x + 265.664 = 510.398825332 Simplifying x + 265.664 = 510.398825332 Reorder the terms: 265.664 + x = 510.398825332 Solving 265.664 + x = 510.398825332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-265.664' to each side of the equation. 265.664 + -265.664 + x = 510.398825332 + -265.664 Combine like terms: 265.664 + -265.664 = 0.000 0.000 + x = 510.398825332 + -265.664 x = 510.398825332 + -265.664 Combine like terms: 510.398825332 + -265.664 = 244.734825332 x = 244.734825332 Simplifying x = 244.734825332Subproblem 2
x + 265.664 = -510.398825332 Simplifying x + 265.664 = -510.398825332 Reorder the terms: 265.664 + x = -510.398825332 Solving 265.664 + x = -510.398825332 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-265.664' to each side of the equation. 265.664 + -265.664 + x = -510.398825332 + -265.664 Combine like terms: 265.664 + -265.664 = 0.000 0.000 + x = -510.398825332 + -265.664 x = -510.398825332 + -265.664 Combine like terms: -510.398825332 + -265.664 = -776.062825332 x = -776.062825332 Simplifying x = -776.062825332Solution
The solution to the problem is based on the solutions from the subproblems. x = {244.734825332, -776.062825332}
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