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Simplifying 3x2 + -320x + 42 = 0 Reorder the terms: 42 + -320x + 3x2 = 0 Solving 42 + -320x + 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'. 14 + -106.6666667x + x2 = 0 Move the constant term to the right: Add '-14' to each side of the equation. 14 + -106.6666667x + -14 + x2 = 0 + -14 Reorder the terms: 14 + -14 + -106.6666667x + x2 = 0 + -14 Combine like terms: 14 + -14 = 0 0 + -106.6666667x + x2 = 0 + -14 -106.6666667x + x2 = 0 + -14 Combine like terms: 0 + -14 = -14 -106.6666667x + x2 = -14 The x term is -106.6666667x. Take half its coefficient (-53.33333335). Square it (2844.444446) and add it to both sides. Add '2844.444446' to each side of the equation. -106.6666667x + 2844.444446 + x2 = -14 + 2844.444446 Reorder the terms: 2844.444446 + -106.6666667x + x2 = -14 + 2844.444446 Combine like terms: -14 + 2844.444446 = 2830.444446 2844.444446 + -106.6666667x + x2 = 2830.444446 Factor a perfect square on the left side: (x + -53.33333335)(x + -53.33333335) = 2830.444446 Calculate the square root of the right side: 53.20192145 Break this problem into two subproblems by setting (x + -53.33333335) equal to 53.20192145 and -53.20192145.Subproblem 1
x + -53.33333335 = 53.20192145 Simplifying x + -53.33333335 = 53.20192145 Reorder the terms: -53.33333335 + x = 53.20192145 Solving -53.33333335 + x = 53.20192145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53.33333335' to each side of the equation. -53.33333335 + 53.33333335 + x = 53.20192145 + 53.33333335 Combine like terms: -53.33333335 + 53.33333335 = 0.00000000 0.00000000 + x = 53.20192145 + 53.33333335 x = 53.20192145 + 53.33333335 Combine like terms: 53.20192145 + 53.33333335 = 106.5352548 x = 106.5352548 Simplifying x = 106.5352548Subproblem 2
x + -53.33333335 = -53.20192145 Simplifying x + -53.33333335 = -53.20192145 Reorder the terms: -53.33333335 + x = -53.20192145 Solving -53.33333335 + x = -53.20192145 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '53.33333335' to each side of the equation. -53.33333335 + 53.33333335 + x = -53.20192145 + 53.33333335 Combine like terms: -53.33333335 + 53.33333335 = 0.00000000 0.00000000 + x = -53.20192145 + 53.33333335 x = -53.20192145 + 53.33333335 Combine like terms: -53.20192145 + 53.33333335 = 0.1314119 x = 0.1314119 Simplifying x = 0.1314119Solution
The solution to the problem is based on the solutions from the subproblems. x = {106.5352548, 0.1314119}
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