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Simplifying 3x2 + -72x + 368 = 0 Reorder the terms: 368 + -72x + 3x2 = 0 Solving 368 + -72x + 3x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. 122.6666667 + -24x + x2 = 0 Move the constant term to the right: Add '-122.6666667' to each side of the equation. 122.6666667 + -24x + -122.6666667 + x2 = 0 + -122.6666667 Reorder the terms: 122.6666667 + -122.6666667 + -24x + x2 = 0 + -122.6666667 Combine like terms: 122.6666667 + -122.6666667 = 0.0000000 0.0000000 + -24x + x2 = 0 + -122.6666667 -24x + x2 = 0 + -122.6666667 Combine like terms: 0 + -122.6666667 = -122.6666667 -24x + x2 = -122.6666667 The x term is -24x. Take half its coefficient (-12). Square it (144) and add it to both sides. Add '144' to each side of the equation. -24x + 144 + x2 = -122.6666667 + 144 Reorder the terms: 144 + -24x + x2 = -122.6666667 + 144 Combine like terms: -122.6666667 + 144 = 21.3333333 144 + -24x + x2 = 21.3333333 Factor a perfect square on the left side: (x + -12)(x + -12) = 21.3333333 Calculate the square root of the right side: 4.61880215 Break this problem into two subproblems by setting (x + -12) equal to 4.61880215 and -4.61880215.Subproblem 1
x + -12 = 4.61880215 Simplifying x + -12 = 4.61880215 Reorder the terms: -12 + x = 4.61880215 Solving -12 + x = 4.61880215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = 4.61880215 + 12 Combine like terms: -12 + 12 = 0 0 + x = 4.61880215 + 12 x = 4.61880215 + 12 Combine like terms: 4.61880215 + 12 = 16.61880215 x = 16.61880215 Simplifying x = 16.61880215Subproblem 2
x + -12 = -4.61880215 Simplifying x + -12 = -4.61880215 Reorder the terms: -12 + x = -4.61880215 Solving -12 + x = -4.61880215 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + x = -4.61880215 + 12 Combine like terms: -12 + 12 = 0 0 + x = -4.61880215 + 12 x = -4.61880215 + 12 Combine like terms: -4.61880215 + 12 = 7.38119785 x = 7.38119785 Simplifying x = 7.38119785Solution
The solution to the problem is based on the solutions from the subproblems. x = {16.61880215, 7.38119785}
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