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Simplifying 0 = 3x2 + -90x + 500 Reorder the terms: 0 = 500 + -90x + 3x2 Solving 0 = 500 + -90x + 3x2 Solving for variable 'x'. Combine like terms: 0 + -500 = -500 -500 + 90x + -3x2 = 500 + -90x + 3x2 + -500 + 90x + -3x2 Reorder the terms: -500 + 90x + -3x2 = 500 + -500 + -90x + 90x + 3x2 + -3x2 Combine like terms: 500 + -500 = 0 -500 + 90x + -3x2 = 0 + -90x + 90x + 3x2 + -3x2 -500 + 90x + -3x2 = -90x + 90x + 3x2 + -3x2 Combine like terms: -90x + 90x = 0 -500 + 90x + -3x2 = 0 + 3x2 + -3x2 -500 + 90x + -3x2 = 3x2 + -3x2 Combine like terms: 3x2 + -3x2 = 0 -500 + 90x + -3x2 = 0 Begin completing the square. Divide all terms by -3 the coefficient of the squared term: Divide each side by '-3'. 166.6666667 + -30x + x2 = 0 Move the constant term to the right: Add '-166.6666667' to each side of the equation. 166.6666667 + -30x + -166.6666667 + x2 = 0 + -166.6666667 Reorder the terms: 166.6666667 + -166.6666667 + -30x + x2 = 0 + -166.6666667 Combine like terms: 166.6666667 + -166.6666667 = 0.0000000 0.0000000 + -30x + x2 = 0 + -166.6666667 -30x + x2 = 0 + -166.6666667 Combine like terms: 0 + -166.6666667 = -166.6666667 -30x + x2 = -166.6666667 The x term is -30x. Take half its coefficient (-15). Square it (225) and add it to both sides. Add '225' to each side of the equation. -30x + 225 + x2 = -166.6666667 + 225 Reorder the terms: 225 + -30x + x2 = -166.6666667 + 225 Combine like terms: -166.6666667 + 225 = 58.3333333 225 + -30x + x2 = 58.3333333 Factor a perfect square on the left side: (x + -15)(x + -15) = 58.3333333 Calculate the square root of the right side: 7.637626156 Break this problem into two subproblems by setting (x + -15) equal to 7.637626156 and -7.637626156.Subproblem 1
x + -15 = 7.637626156 Simplifying x + -15 = 7.637626156 Reorder the terms: -15 + x = 7.637626156 Solving -15 + x = 7.637626156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = 7.637626156 + 15 Combine like terms: -15 + 15 = 0 0 + x = 7.637626156 + 15 x = 7.637626156 + 15 Combine like terms: 7.637626156 + 15 = 22.637626156 x = 22.637626156 Simplifying x = 22.637626156Subproblem 2
x + -15 = -7.637626156 Simplifying x + -15 = -7.637626156 Reorder the terms: -15 + x = -7.637626156 Solving -15 + x = -7.637626156 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '15' to each side of the equation. -15 + 15 + x = -7.637626156 + 15 Combine like terms: -15 + 15 = 0 0 + x = -7.637626156 + 15 x = -7.637626156 + 15 Combine like terms: -7.637626156 + 15 = 7.362373844 x = 7.362373844 Simplifying x = 7.362373844Solution
The solution to the problem is based on the solutions from the subproblems. x = {22.637626156, 7.362373844}
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