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Simplifying -1x2 + 46x + -30 = 0 Reorder the terms: -30 + 46x + -1x2 = 0 Solving -30 + 46x + -1x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 30 + -46x + x2 = 0 Move the constant term to the right: Add '-30' to each side of the equation. 30 + -46x + -30 + x2 = 0 + -30 Reorder the terms: 30 + -30 + -46x + x2 = 0 + -30 Combine like terms: 30 + -30 = 0 0 + -46x + x2 = 0 + -30 -46x + x2 = 0 + -30 Combine like terms: 0 + -30 = -30 -46x + x2 = -30 The x term is -46x. Take half its coefficient (-23). Square it (529) and add it to both sides. Add '529' to each side of the equation. -46x + 529 + x2 = -30 + 529 Reorder the terms: 529 + -46x + x2 = -30 + 529 Combine like terms: -30 + 529 = 499 529 + -46x + x2 = 499 Factor a perfect square on the left side: (x + -23)(x + -23) = 499 Calculate the square root of the right side: 22.338307904 Break this problem into two subproblems by setting (x + -23) equal to 22.338307904 and -22.338307904.Subproblem 1
x + -23 = 22.338307904 Simplifying x + -23 = 22.338307904 Reorder the terms: -23 + x = 22.338307904 Solving -23 + x = 22.338307904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = 22.338307904 + 23 Combine like terms: -23 + 23 = 0 0 + x = 22.338307904 + 23 x = 22.338307904 + 23 Combine like terms: 22.338307904 + 23 = 45.338307904 x = 45.338307904 Simplifying x = 45.338307904Subproblem 2
x + -23 = -22.338307904 Simplifying x + -23 = -22.338307904 Reorder the terms: -23 + x = -22.338307904 Solving -23 + x = -22.338307904 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '23' to each side of the equation. -23 + 23 + x = -22.338307904 + 23 Combine like terms: -23 + 23 = 0 0 + x = -22.338307904 + 23 x = -22.338307904 + 23 Combine like terms: -22.338307904 + 23 = 0.661692096 x = 0.661692096 Simplifying x = 0.661692096Solution
The solution to the problem is based on the solutions from the subproblems. x = {45.338307904, 0.661692096}
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