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Simplifying x2 + 35.5x + -357 = 0 Reorder the terms: -357 + 35.5x + x2 = 0 Solving -357 + 35.5x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '357' to each side of the equation. -357 + 35.5x + 357 + x2 = 0 + 357 Reorder the terms: -357 + 357 + 35.5x + x2 = 0 + 357 Combine like terms: -357 + 357 = 0 0 + 35.5x + x2 = 0 + 357 35.5x + x2 = 0 + 357 Combine like terms: 0 + 357 = 357 35.5x + x2 = 357 The x term is 35.5x. Take half its coefficient (17.75). Square it (315.0625) and add it to both sides. Add '315.0625' to each side of the equation. 35.5x + 315.0625 + x2 = 357 + 315.0625 Reorder the terms: 315.0625 + 35.5x + x2 = 357 + 315.0625 Combine like terms: 357 + 315.0625 = 672.0625 315.0625 + 35.5x + x2 = 672.0625 Factor a perfect square on the left side: (x + 17.75)(x + 17.75) = 672.0625 Calculate the square root of the right side: 25.924168261 Break this problem into two subproblems by setting (x + 17.75) equal to 25.924168261 and -25.924168261.Subproblem 1
x + 17.75 = 25.924168261 Simplifying x + 17.75 = 25.924168261 Reorder the terms: 17.75 + x = 25.924168261 Solving 17.75 + x = 25.924168261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.75' to each side of the equation. 17.75 + -17.75 + x = 25.924168261 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + x = 25.924168261 + -17.75 x = 25.924168261 + -17.75 Combine like terms: 25.924168261 + -17.75 = 8.174168261 x = 8.174168261 Simplifying x = 8.174168261Subproblem 2
x + 17.75 = -25.924168261 Simplifying x + 17.75 = -25.924168261 Reorder the terms: 17.75 + x = -25.924168261 Solving 17.75 + x = -25.924168261 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-17.75' to each side of the equation. 17.75 + -17.75 + x = -25.924168261 + -17.75 Combine like terms: 17.75 + -17.75 = 0.00 0.00 + x = -25.924168261 + -17.75 x = -25.924168261 + -17.75 Combine like terms: -25.924168261 + -17.75 = -43.674168261 x = -43.674168261 Simplifying x = -43.674168261Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.174168261, -43.674168261}
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