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Simplifying -3x2 + 30x + -41 = 0 Reorder the terms: -41 + 30x + -3x2 = 0 Solving -41 + 30x + -3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 13.66666667 + -10x + x2 = 0 Move the constant term to the right: Add '-13.66666667' to each side of the equation. 13.66666667 + -10x + -13.66666667 + x2 = 0 + -13.66666667 Reorder the terms: 13.66666667 + -13.66666667 + -10x + x2 = 0 + -13.66666667 Combine like terms: 13.66666667 + -13.66666667 = 0.00000000 0.00000000 + -10x + x2 = 0 + -13.66666667 -10x + x2 = 0 + -13.66666667 Combine like terms: 0 + -13.66666667 = -13.66666667 -10x + x2 = -13.66666667 The x term is -10x. Take half its coefficient (-5). Square it (25) and add it to both sides. Add '25' to each side of the equation. -10x + 25 + x2 = -13.66666667 + 25 Reorder the terms: 25 + -10x + x2 = -13.66666667 + 25 Combine like terms: -13.66666667 + 25 = 11.33333333 25 + -10x + x2 = 11.33333333 Factor a perfect square on the left side: (x + -5)(x + -5) = 11.33333333 Calculate the square root of the right side: 3.366501646 Break this problem into two subproblems by setting (x + -5) equal to 3.366501646 and -3.366501646.Subproblem 1
x + -5 = 3.366501646 Simplifying x + -5 = 3.366501646 Reorder the terms: -5 + x = 3.366501646 Solving -5 + x = 3.366501646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = 3.366501646 + 5 Combine like terms: -5 + 5 = 0 0 + x = 3.366501646 + 5 x = 3.366501646 + 5 Combine like terms: 3.366501646 + 5 = 8.366501646 x = 8.366501646 Simplifying x = 8.366501646Subproblem 2
x + -5 = -3.366501646 Simplifying x + -5 = -3.366501646 Reorder the terms: -5 + x = -3.366501646 Solving -5 + x = -3.366501646 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + x = -3.366501646 + 5 Combine like terms: -5 + 5 = 0 0 + x = -3.366501646 + 5 x = -3.366501646 + 5 Combine like terms: -3.366501646 + 5 = 1.633498354 x = 1.633498354 Simplifying x = 1.633498354Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.366501646, 1.633498354}
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