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Simplifying 3x2 + -10x + -450 = 0 Reorder the terms: -450 + -10x + 3x2 = 0 Solving -450 + -10x + 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'. -150 + -3.333333333x + x2 = 0 Move the constant term to the right: Add '150' to each side of the equation. -150 + -3.333333333x + 150 + x2 = 0 + 150 Reorder the terms: -150 + 150 + -3.333333333x + x2 = 0 + 150 Combine like terms: -150 + 150 = 0 0 + -3.333333333x + x2 = 0 + 150 -3.333333333x + x2 = 0 + 150 Combine like terms: 0 + 150 = 150 -3.333333333x + x2 = 150 The x term is -3.333333333x. Take half its coefficient (-1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. -3.333333333x + 2.777777779 + x2 = 150 + 2.777777779 Reorder the terms: 2.777777779 + -3.333333333x + x2 = 150 + 2.777777779 Combine like terms: 150 + 2.777777779 = 152.777777779 2.777777779 + -3.333333333x + x2 = 152.777777779 Factor a perfect square on the left side: (x + -1.666666667)(x + -1.666666667) = 152.777777779 Calculate the square root of the right side: 12.360330812 Break this problem into two subproblems by setting (x + -1.666666667) equal to 12.360330812 and -12.360330812.Subproblem 1
x + -1.666666667 = 12.360330812 Simplifying x + -1.666666667 = 12.360330812 Reorder the terms: -1.666666667 + x = 12.360330812 Solving -1.666666667 + x = 12.360330812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = 12.360330812 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = 12.360330812 + 1.666666667 x = 12.360330812 + 1.666666667 Combine like terms: 12.360330812 + 1.666666667 = 14.026997479 x = 14.026997479 Simplifying x = 14.026997479Subproblem 2
x + -1.666666667 = -12.360330812 Simplifying x + -1.666666667 = -12.360330812 Reorder the terms: -1.666666667 + x = -12.360330812 Solving -1.666666667 + x = -12.360330812 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.666666667' to each side of the equation. -1.666666667 + 1.666666667 + x = -12.360330812 + 1.666666667 Combine like terms: -1.666666667 + 1.666666667 = 0.000000000 0.000000000 + x = -12.360330812 + 1.666666667 x = -12.360330812 + 1.666666667 Combine like terms: -12.360330812 + 1.666666667 = -10.693664145 x = -10.693664145 Simplifying x = -10.693664145Solution
The solution to the problem is based on the solutions from the subproblems. x = {14.026997479, -10.693664145}
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