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Simplifying 3x2 + -72x + 320 = 0 Reorder the terms: 320 + -72x + 3x2 = 0 Solving 320 + -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'. 106.6666667 + -24x + x2 = 0 Move the constant term to the right: Add '-106.6666667' to each side of the equation. 106.6666667 + -24x + -106.6666667 + x2 = 0 + -106.6666667 Reorder the terms: 106.6666667 + -106.6666667 + -24x + x2 = 0 + -106.6666667 Combine like terms: 106.6666667 + -106.6666667 = 0.0000000 0.0000000 + -24x + x2 = 0 + -106.6666667 -24x + x2 = 0 + -106.6666667 Combine like terms: 0 + -106.6666667 = -106.6666667 -24x + x2 = -106.6666667 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 = -106.6666667 + 144 Reorder the terms: 144 + -24x + x2 = -106.6666667 + 144 Combine like terms: -106.6666667 + 144 = 37.3333333 144 + -24x + x2 = 37.3333333 Factor a perfect square on the left side: (x + -12)(x + -12) = 37.3333333 Calculate the square root of the right side: 6.110100924 Break this problem into two subproblems by setting (x + -12) equal to 6.110100924 and -6.110100924.Subproblem 1
x + -12 = 6.110100924 Simplifying x + -12 = 6.110100924 Reorder the terms: -12 + x = 6.110100924 Solving -12 + x = 6.110100924 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 = 6.110100924 + 12 Combine like terms: -12 + 12 = 0 0 + x = 6.110100924 + 12 x = 6.110100924 + 12 Combine like terms: 6.110100924 + 12 = 18.110100924 x = 18.110100924 Simplifying x = 18.110100924Subproblem 2
x + -12 = -6.110100924 Simplifying x + -12 = -6.110100924 Reorder the terms: -12 + x = -6.110100924 Solving -12 + x = -6.110100924 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 = -6.110100924 + 12 Combine like terms: -12 + 12 = 0 0 + x = -6.110100924 + 12 x = -6.110100924 + 12 Combine like terms: -6.110100924 + 12 = 5.889899076 x = 5.889899076 Simplifying x = 5.889899076Solution
The solution to the problem is based on the solutions from the subproblems. x = {18.110100924, 5.889899076}
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