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Simplifying -3x2 + 241x + -325 = 0 Reorder the terms: -325 + 241x + -3x2 = 0 Solving -325 + 241x + -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'. 108.3333333 + -80.33333333x + x2 = 0 Move the constant term to the right: Add '-108.3333333' to each side of the equation. 108.3333333 + -80.33333333x + -108.3333333 + x2 = 0 + -108.3333333 Reorder the terms: 108.3333333 + -108.3333333 + -80.33333333x + x2 = 0 + -108.3333333 Combine like terms: 108.3333333 + -108.3333333 = 0.0000000 0.0000000 + -80.33333333x + x2 = 0 + -108.3333333 -80.33333333x + x2 = 0 + -108.3333333 Combine like terms: 0 + -108.3333333 = -108.3333333 -80.33333333x + x2 = -108.3333333 The x term is -80.33333333x. Take half its coefficient (-40.16666667). Square it (1613.361111) and add it to both sides. Add '1613.361111' to each side of the equation. -80.33333333x + 1613.361111 + x2 = -108.3333333 + 1613.361111 Reorder the terms: 1613.361111 + -80.33333333x + x2 = -108.3333333 + 1613.361111 Combine like terms: -108.3333333 + 1613.361111 = 1505.0277777 1613.361111 + -80.33333333x + x2 = 1505.0277777 Factor a perfect square on the left side: (x + -40.16666667)(x + -40.16666667) = 1505.0277777 Calculate the square root of the right side: 38.794687493 Break this problem into two subproblems by setting (x + -40.16666667) equal to 38.794687493 and -38.794687493.Subproblem 1
x + -40.16666667 = 38.794687493 Simplifying x + -40.16666667 = 38.794687493 Reorder the terms: -40.16666667 + x = 38.794687493 Solving -40.16666667 + x = 38.794687493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.16666667' to each side of the equation. -40.16666667 + 40.16666667 + x = 38.794687493 + 40.16666667 Combine like terms: -40.16666667 + 40.16666667 = 0.00000000 0.00000000 + x = 38.794687493 + 40.16666667 x = 38.794687493 + 40.16666667 Combine like terms: 38.794687493 + 40.16666667 = 78.961354163 x = 78.961354163 Simplifying x = 78.961354163Subproblem 2
x + -40.16666667 = -38.794687493 Simplifying x + -40.16666667 = -38.794687493 Reorder the terms: -40.16666667 + x = -38.794687493 Solving -40.16666667 + x = -38.794687493 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '40.16666667' to each side of the equation. -40.16666667 + 40.16666667 + x = -38.794687493 + 40.16666667 Combine like terms: -40.16666667 + 40.16666667 = 0.00000000 0.00000000 + x = -38.794687493 + 40.16666667 x = -38.794687493 + 40.16666667 Combine like terms: -38.794687493 + 40.16666667 = 1.371979177 x = 1.371979177 Simplifying x = 1.371979177Solution
The solution to the problem is based on the solutions from the subproblems. x = {78.961354163, 1.371979177}
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