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Simplifying 0.09x2 + -30x + 600 = 0 Reorder the terms: 600 + -30x + 0.09x2 = 0 Solving 600 + -30x + 0.09x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 0.09 the coefficient of the squared term: Divide each side by '0.09'. 6666.666667 + -333.3333333x + x2 = 0 Move the constant term to the right: Add '-6666.666667' to each side of the equation. 6666.666667 + -333.3333333x + -6666.666667 + x2 = 0 + -6666.666667 Reorder the terms: 6666.666667 + -6666.666667 + -333.3333333x + x2 = 0 + -6666.666667 Combine like terms: 6666.666667 + -6666.666667 = 0.000000 0.000000 + -333.3333333x + x2 = 0 + -6666.666667 -333.3333333x + x2 = 0 + -6666.666667 Combine like terms: 0 + -6666.666667 = -6666.666667 -333.3333333x + x2 = -6666.666667 The x term is -333.3333333x. Take half its coefficient (-166.6666667). Square it (27777.77779) and add it to both sides. Add '27777.77779' to each side of the equation. -333.3333333x + 27777.77779 + x2 = -6666.666667 + 27777.77779 Reorder the terms: 27777.77779 + -333.3333333x + x2 = -6666.666667 + 27777.77779 Combine like terms: -6666.666667 + 27777.77779 = 21111.111123 27777.77779 + -333.3333333x + x2 = 21111.111123 Factor a perfect square on the left side: (x + -166.6666667)(x + -166.6666667) = 21111.111123 Calculate the square root of the right side: 145.296631492 Break this problem into two subproblems by setting (x + -166.6666667) equal to 145.296631492 and -145.296631492.Subproblem 1
x + -166.6666667 = 145.296631492 Simplifying x + -166.6666667 = 145.296631492 Reorder the terms: -166.6666667 + x = 145.296631492 Solving -166.6666667 + x = 145.296631492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.6666667' to each side of the equation. -166.6666667 + 166.6666667 + x = 145.296631492 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + x = 145.296631492 + 166.6666667 x = 145.296631492 + 166.6666667 Combine like terms: 145.296631492 + 166.6666667 = 311.963298192 x = 311.963298192 Simplifying x = 311.963298192Subproblem 2
x + -166.6666667 = -145.296631492 Simplifying x + -166.6666667 = -145.296631492 Reorder the terms: -166.6666667 + x = -145.296631492 Solving -166.6666667 + x = -145.296631492 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '166.6666667' to each side of the equation. -166.6666667 + 166.6666667 + x = -145.296631492 + 166.6666667 Combine like terms: -166.6666667 + 166.6666667 = 0.0000000 0.0000000 + x = -145.296631492 + 166.6666667 x = -145.296631492 + 166.6666667 Combine like terms: -145.296631492 + 166.6666667 = 21.370035208 x = 21.370035208 Simplifying x = 21.370035208Solution
The solution to the problem is based on the solutions from the subproblems. x = {311.963298192, 21.370035208}
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