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Simplifying 12x2 + -360x + 2000 = 0 Reorder the terms: 2000 + -360x + 12x2 = 0 Solving 2000 + -360x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '4'. 4(500 + -90x + 3x2) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(500 + -90x + 3x2)' equal to zero and attempt to solve: Simplifying 500 + -90x + 3x2 = 0 Solving 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}Solution
x = {22.637626156, 7.362373844}
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