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Simplifying 3x2 + -1x = 300 Reorder the terms: -1x + 3x2 = 300 Solving -1x + 3x2 = 300 Solving for variable 'x'. Reorder the terms: -300 + -1x + 3x2 = 300 + -300 Combine like terms: 300 + -300 = 0 -300 + -1x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -100 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '100' to each side of the equation. -100 + -0.3333333333x + 100 + x2 = 0 + 100 Reorder the terms: -100 + 100 + -0.3333333333x + x2 = 0 + 100 Combine like terms: -100 + 100 = 0 0 + -0.3333333333x + x2 = 0 + 100 -0.3333333333x + x2 = 0 + 100 Combine like terms: 0 + 100 = 100 -0.3333333333x + x2 = 100 The x term is -0.3333333333x. Take half its coefficient (-0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. -0.3333333333x + 0.02777777779 + x2 = 100 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 100 + 0.02777777779 Combine like terms: 100 + 0.02777777779 = 100.02777777779 0.02777777779 + -0.3333333333x + x2 = 100.02777777779 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 100.02777777779 Calculate the square root of the right side: 10.001388792 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 10.001388792 and -10.001388792.Subproblem 1
x + -0.1666666667 = 10.001388792 Simplifying x + -0.1666666667 = 10.001388792 Reorder the terms: -0.1666666667 + x = 10.001388792 Solving -0.1666666667 + x = 10.001388792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = 10.001388792 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 10.001388792 + 0.1666666667 x = 10.001388792 + 0.1666666667 Combine like terms: 10.001388792 + 0.1666666667 = 10.1680554587 x = 10.1680554587 Simplifying x = 10.1680554587Subproblem 2
x + -0.1666666667 = -10.001388792 Simplifying x + -0.1666666667 = -10.001388792 Reorder the terms: -0.1666666667 + x = -10.001388792 Solving -0.1666666667 + x = -10.001388792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.1666666667' to each side of the equation. -0.1666666667 + 0.1666666667 + x = -10.001388792 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -10.001388792 + 0.1666666667 x = -10.001388792 + 0.1666666667 Combine like terms: -10.001388792 + 0.1666666667 = -9.8347221253 x = -9.8347221253 Simplifying x = -9.8347221253Solution
The solution to the problem is based on the solutions from the subproblems. x = {10.1680554587, -9.8347221253}
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