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Simplifying x2 + -34x = 280 Reorder the terms: -34x + x2 = 280 Solving -34x + x2 = 280 Solving for variable 'x'. Reorder the terms: -280 + -34x + x2 = 280 + -280 Combine like terms: 280 + -280 = 0 -280 + -34x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '280' to each side of the equation. -280 + -34x + 280 + x2 = 0 + 280 Reorder the terms: -280 + 280 + -34x + x2 = 0 + 280 Combine like terms: -280 + 280 = 0 0 + -34x + x2 = 0 + 280 -34x + x2 = 0 + 280 Combine like terms: 0 + 280 = 280 -34x + x2 = 280 The x term is -34x. Take half its coefficient (-17). Square it (289) and add it to both sides. Add '289' to each side of the equation. -34x + 289 + x2 = 280 + 289 Reorder the terms: 289 + -34x + x2 = 280 + 289 Combine like terms: 280 + 289 = 569 289 + -34x + x2 = 569 Factor a perfect square on the left side: (x + -17)(x + -17) = 569 Calculate the square root of the right side: 23.853720884 Break this problem into two subproblems by setting (x + -17) equal to 23.853720884 and -23.853720884.Subproblem 1
x + -17 = 23.853720884 Simplifying x + -17 = 23.853720884 Reorder the terms: -17 + x = 23.853720884 Solving -17 + x = 23.853720884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = 23.853720884 + 17 Combine like terms: -17 + 17 = 0 0 + x = 23.853720884 + 17 x = 23.853720884 + 17 Combine like terms: 23.853720884 + 17 = 40.853720884 x = 40.853720884 Simplifying x = 40.853720884Subproblem 2
x + -17 = -23.853720884 Simplifying x + -17 = -23.853720884 Reorder the terms: -17 + x = -23.853720884 Solving -17 + x = -23.853720884 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '17' to each side of the equation. -17 + 17 + x = -23.853720884 + 17 Combine like terms: -17 + 17 = 0 0 + x = -23.853720884 + 17 x = -23.853720884 + 17 Combine like terms: -23.853720884 + 17 = -6.853720884 x = -6.853720884 Simplifying x = -6.853720884Solution
The solution to the problem is based on the solutions from the subproblems. x = {40.853720884, -6.853720884}
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