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Simplifying 21x2 + -156x + 7 = 0 Reorder the terms: 7 + -156x + 21x2 = 0 Solving 7 + -156x + 21x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. 0.3333333333 + -7.428571429x + x2 = 0 Move the constant term to the right: Add '-0.3333333333' to each side of the equation. 0.3333333333 + -7.428571429x + -0.3333333333 + x2 = 0 + -0.3333333333 Reorder the terms: 0.3333333333 + -0.3333333333 + -7.428571429x + x2 = 0 + -0.3333333333 Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000 0.0000000000 + -7.428571429x + x2 = 0 + -0.3333333333 -7.428571429x + x2 = 0 + -0.3333333333 Combine like terms: 0 + -0.3333333333 = -0.3333333333 -7.428571429x + x2 = -0.3333333333 The x term is -7.428571429x. Take half its coefficient (-3.714285715). Square it (13.79591837) and add it to both sides. Add '13.79591837' to each side of the equation. -7.428571429x + 13.79591837 + x2 = -0.3333333333 + 13.79591837 Reorder the terms: 13.79591837 + -7.428571429x + x2 = -0.3333333333 + 13.79591837 Combine like terms: -0.3333333333 + 13.79591837 = 13.4625850367 13.79591837 + -7.428571429x + x2 = 13.4625850367 Factor a perfect square on the left side: (x + -3.714285715)(x + -3.714285715) = 13.4625850367 Calculate the square root of the right side: 3.66913955 Break this problem into two subproblems by setting (x + -3.714285715) equal to 3.66913955 and -3.66913955.Subproblem 1
x + -3.714285715 = 3.66913955 Simplifying x + -3.714285715 = 3.66913955 Reorder the terms: -3.714285715 + x = 3.66913955 Solving -3.714285715 + x = 3.66913955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.714285715' to each side of the equation. -3.714285715 + 3.714285715 + x = 3.66913955 + 3.714285715 Combine like terms: -3.714285715 + 3.714285715 = 0.000000000 0.000000000 + x = 3.66913955 + 3.714285715 x = 3.66913955 + 3.714285715 Combine like terms: 3.66913955 + 3.714285715 = 7.383425265 x = 7.383425265 Simplifying x = 7.383425265Subproblem 2
x + -3.714285715 = -3.66913955 Simplifying x + -3.714285715 = -3.66913955 Reorder the terms: -3.714285715 + x = -3.66913955 Solving -3.714285715 + x = -3.66913955 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.714285715' to each side of the equation. -3.714285715 + 3.714285715 + x = -3.66913955 + 3.714285715 Combine like terms: -3.714285715 + 3.714285715 = 0.000000000 0.000000000 + x = -3.66913955 + 3.714285715 x = -3.66913955 + 3.714285715 Combine like terms: -3.66913955 + 3.714285715 = 0.045146165 x = 0.045146165 Simplifying x = 0.045146165Solution
The solution to the problem is based on the solutions from the subproblems. x = {7.383425265, 0.045146165}
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