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Simplifying x2 + -86x = 249 Reorder the terms: -86x + x2 = 249 Solving -86x + x2 = 249 Solving for variable 'x'. Reorder the terms: -249 + -86x + x2 = 249 + -249 Combine like terms: 249 + -249 = 0 -249 + -86x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '249' to each side of the equation. -249 + -86x + 249 + x2 = 0 + 249 Reorder the terms: -249 + 249 + -86x + x2 = 0 + 249 Combine like terms: -249 + 249 = 0 0 + -86x + x2 = 0 + 249 -86x + x2 = 0 + 249 Combine like terms: 0 + 249 = 249 -86x + x2 = 249 The x term is -86x. Take half its coefficient (-43). Square it (1849) and add it to both sides. Add '1849' to each side of the equation. -86x + 1849 + x2 = 249 + 1849 Reorder the terms: 1849 + -86x + x2 = 249 + 1849 Combine like terms: 249 + 1849 = 2098 1849 + -86x + x2 = 2098 Factor a perfect square on the left side: (x + -43)(x + -43) = 2098 Calculate the square root of the right side: 45.803929962 Break this problem into two subproblems by setting (x + -43) equal to 45.803929962 and -45.803929962.Subproblem 1
x + -43 = 45.803929962 Simplifying x + -43 = 45.803929962 Reorder the terms: -43 + x = 45.803929962 Solving -43 + x = 45.803929962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + x = 45.803929962 + 43 Combine like terms: -43 + 43 = 0 0 + x = 45.803929962 + 43 x = 45.803929962 + 43 Combine like terms: 45.803929962 + 43 = 88.803929962 x = 88.803929962 Simplifying x = 88.803929962Subproblem 2
x + -43 = -45.803929962 Simplifying x + -43 = -45.803929962 Reorder the terms: -43 + x = -45.803929962 Solving -43 + x = -45.803929962 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '43' to each side of the equation. -43 + 43 + x = -45.803929962 + 43 Combine like terms: -43 + 43 = 0 0 + x = -45.803929962 + 43 x = -45.803929962 + 43 Combine like terms: -45.803929962 + 43 = -2.803929962 x = -2.803929962 Simplifying x = -2.803929962Solution
The solution to the problem is based on the solutions from the subproblems. x = {88.803929962, -2.803929962}
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