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Simplifying x2 + -100x + 330 = 0 Reorder the terms: 330 + -100x + x2 = 0 Solving 330 + -100x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-330' to each side of the equation. 330 + -100x + -330 + x2 = 0 + -330 Reorder the terms: 330 + -330 + -100x + x2 = 0 + -330 Combine like terms: 330 + -330 = 0 0 + -100x + x2 = 0 + -330 -100x + x2 = 0 + -330 Combine like terms: 0 + -330 = -330 -100x + x2 = -330 The x term is -100x. Take half its coefficient (-50). Square it (2500) and add it to both sides. Add '2500' to each side of the equation. -100x + 2500 + x2 = -330 + 2500 Reorder the terms: 2500 + -100x + x2 = -330 + 2500 Combine like terms: -330 + 2500 = 2170 2500 + -100x + x2 = 2170 Factor a perfect square on the left side: (x + -50)(x + -50) = 2170 Calculate the square root of the right side: 46.583258795 Break this problem into two subproblems by setting (x + -50) equal to 46.583258795 and -46.583258795.Subproblem 1
x + -50 = 46.583258795 Simplifying x + -50 = 46.583258795 Reorder the terms: -50 + x = 46.583258795 Solving -50 + x = 46.583258795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = 46.583258795 + 50 Combine like terms: -50 + 50 = 0 0 + x = 46.583258795 + 50 x = 46.583258795 + 50 Combine like terms: 46.583258795 + 50 = 96.583258795 x = 96.583258795 Simplifying x = 96.583258795Subproblem 2
x + -50 = -46.583258795 Simplifying x + -50 = -46.583258795 Reorder the terms: -50 + x = -46.583258795 Solving -50 + x = -46.583258795 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '50' to each side of the equation. -50 + 50 + x = -46.583258795 + 50 Combine like terms: -50 + 50 = 0 0 + x = -46.583258795 + 50 x = -46.583258795 + 50 Combine like terms: -46.583258795 + 50 = 3.416741205 x = 3.416741205 Simplifying x = 3.416741205Solution
The solution to the problem is based on the solutions from the subproblems. x = {96.583258795, 3.416741205}
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