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Simplifying 3x2 + -77x + 18 = 0 Reorder the terms: 18 + -77x + 3x2 = 0 Solving 18 + -77x + 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'. 6 + -25.66666667x + x2 = 0 Move the constant term to the right: Add '-6' to each side of the equation. 6 + -25.66666667x + -6 + x2 = 0 + -6 Reorder the terms: 6 + -6 + -25.66666667x + x2 = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -25.66666667x + x2 = 0 + -6 -25.66666667x + x2 = 0 + -6 Combine like terms: 0 + -6 = -6 -25.66666667x + x2 = -6 The x term is -25.66666667x. Take half its coefficient (-12.83333334). Square it (164.6944446) and add it to both sides. Add '164.6944446' to each side of the equation. -25.66666667x + 164.6944446 + x2 = -6 + 164.6944446 Reorder the terms: 164.6944446 + -25.66666667x + x2 = -6 + 164.6944446 Combine like terms: -6 + 164.6944446 = 158.6944446 164.6944446 + -25.66666667x + x2 = 158.6944446 Factor a perfect square on the left side: (x + -12.83333334)(x + -12.83333334) = 158.6944446 Calculate the square root of the right side: 12.597398327 Break this problem into two subproblems by setting (x + -12.83333334) equal to 12.597398327 and -12.597398327.Subproblem 1
x + -12.83333334 = 12.597398327 Simplifying x + -12.83333334 = 12.597398327 Reorder the terms: -12.83333334 + x = 12.597398327 Solving -12.83333334 + x = 12.597398327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.83333334' to each side of the equation. -12.83333334 + 12.83333334 + x = 12.597398327 + 12.83333334 Combine like terms: -12.83333334 + 12.83333334 = 0.00000000 0.00000000 + x = 12.597398327 + 12.83333334 x = 12.597398327 + 12.83333334 Combine like terms: 12.597398327 + 12.83333334 = 25.430731667 x = 25.430731667 Simplifying x = 25.430731667Subproblem 2
x + -12.83333334 = -12.597398327 Simplifying x + -12.83333334 = -12.597398327 Reorder the terms: -12.83333334 + x = -12.597398327 Solving -12.83333334 + x = -12.597398327 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12.83333334' to each side of the equation. -12.83333334 + 12.83333334 + x = -12.597398327 + 12.83333334 Combine like terms: -12.83333334 + 12.83333334 = 0.00000000 0.00000000 + x = -12.597398327 + 12.83333334 x = -12.597398327 + 12.83333334 Combine like terms: -12.597398327 + 12.83333334 = 0.235935013 x = 0.235935013 Simplifying x = 0.235935013Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.430731667, 0.235935013}
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