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Simplifying x2 + -389x + 1790 = 0 Reorder the terms: 1790 + -389x + x2 = 0 Solving 1790 + -389x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-1790' to each side of the equation. 1790 + -389x + -1790 + x2 = 0 + -1790 Reorder the terms: 1790 + -1790 + -389x + x2 = 0 + -1790 Combine like terms: 1790 + -1790 = 0 0 + -389x + x2 = 0 + -1790 -389x + x2 = 0 + -1790 Combine like terms: 0 + -1790 = -1790 -389x + x2 = -1790 The x term is -389x. Take half its coefficient (-194.5). Square it (37830.25) and add it to both sides. Add '37830.25' to each side of the equation. -389x + 37830.25 + x2 = -1790 + 37830.25 Reorder the terms: 37830.25 + -389x + x2 = -1790 + 37830.25 Combine like terms: -1790 + 37830.25 = 36040.25 37830.25 + -389x + x2 = 36040.25 Factor a perfect square on the left side: (x + -194.5)(x + -194.5) = 36040.25 Calculate the square root of the right side: 189.842698042 Break this problem into two subproblems by setting (x + -194.5) equal to 189.842698042 and -189.842698042.Subproblem 1
x + -194.5 = 189.842698042 Simplifying x + -194.5 = 189.842698042 Reorder the terms: -194.5 + x = 189.842698042 Solving -194.5 + x = 189.842698042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '194.5' to each side of the equation. -194.5 + 194.5 + x = 189.842698042 + 194.5 Combine like terms: -194.5 + 194.5 = 0.0 0.0 + x = 189.842698042 + 194.5 x = 189.842698042 + 194.5 Combine like terms: 189.842698042 + 194.5 = 384.342698042 x = 384.342698042 Simplifying x = 384.342698042Subproblem 2
x + -194.5 = -189.842698042 Simplifying x + -194.5 = -189.842698042 Reorder the terms: -194.5 + x = -189.842698042 Solving -194.5 + x = -189.842698042 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '194.5' to each side of the equation. -194.5 + 194.5 + x = -189.842698042 + 194.5 Combine like terms: -194.5 + 194.5 = 0.0 0.0 + x = -189.842698042 + 194.5 x = -189.842698042 + 194.5 Combine like terms: -189.842698042 + 194.5 = 4.657301958 x = 4.657301958 Simplifying x = 4.657301958Solution
The solution to the problem is based on the solutions from the subproblems. x = {384.342698042, 4.657301958}
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