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Simplifying 12x2 + -240x + 819 = 0 Reorder the terms: 819 + -240x + 12x2 = 0 Solving 819 + -240x + 12x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '3'. 3(273 + -80x + 4x2) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(273 + -80x + 4x2)' equal to zero and attempt to solve: Simplifying 273 + -80x + 4x2 = 0 Solving 273 + -80x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. 68.25 + -20x + x2 = 0 Move the constant term to the right: Add '-68.25' to each side of the equation. 68.25 + -20x + -68.25 + x2 = 0 + -68.25 Reorder the terms: 68.25 + -68.25 + -20x + x2 = 0 + -68.25 Combine like terms: 68.25 + -68.25 = 0.00 0.00 + -20x + x2 = 0 + -68.25 -20x + x2 = 0 + -68.25 Combine like terms: 0 + -68.25 = -68.25 -20x + x2 = -68.25 The x term is -20x. Take half its coefficient (-10). Square it (100) and add it to both sides. Add '100' to each side of the equation. -20x + 100 + x2 = -68.25 + 100 Reorder the terms: 100 + -20x + x2 = -68.25 + 100 Combine like terms: -68.25 + 100 = 31.75 100 + -20x + x2 = 31.75 Factor a perfect square on the left side: (x + -10)(x + -10) = 31.75 Calculate the square root of the right side: 5.634713835 Break this problem into two subproblems by setting (x + -10) equal to 5.634713835 and -5.634713835.Subproblem 1
x + -10 = 5.634713835 Simplifying x + -10 = 5.634713835 Reorder the terms: -10 + x = 5.634713835 Solving -10 + x = 5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = 5.634713835 + 10 Combine like terms: -10 + 10 = 0 0 + x = 5.634713835 + 10 x = 5.634713835 + 10 Combine like terms: 5.634713835 + 10 = 15.634713835 x = 15.634713835 Simplifying x = 15.634713835Subproblem 2
x + -10 = -5.634713835 Simplifying x + -10 = -5.634713835 Reorder the terms: -10 + x = -5.634713835 Solving -10 + x = -5.634713835 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + x = -5.634713835 + 10 Combine like terms: -10 + 10 = 0 0 + x = -5.634713835 + 10 x = -5.634713835 + 10 Combine like terms: -5.634713835 + 10 = 4.365286165 x = 4.365286165 Simplifying x = 4.365286165Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.634713835, 4.365286165}Solution
x = {15.634713835, 4.365286165}
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