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Simplifying 7x2 + -28x + 1 = 0 Reorder the terms: 1 + -28x + 7x2 = 0 Solving 1 + -28x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. 0.1428571429 + -4x + x2 = 0 Move the constant term to the right: Add '-0.1428571429' to each side of the equation. 0.1428571429 + -4x + -0.1428571429 + x2 = 0 + -0.1428571429 Reorder the terms: 0.1428571429 + -0.1428571429 + -4x + x2 = 0 + -0.1428571429 Combine like terms: 0.1428571429 + -0.1428571429 = 0.0000000000 0.0000000000 + -4x + x2 = 0 + -0.1428571429 -4x + x2 = 0 + -0.1428571429 Combine like terms: 0 + -0.1428571429 = -0.1428571429 -4x + x2 = -0.1428571429 The x term is -4x. Take half its coefficient (-2). Square it (4) and add it to both sides. Add '4' to each side of the equation. -4x + 4 + x2 = -0.1428571429 + 4 Reorder the terms: 4 + -4x + x2 = -0.1428571429 + 4 Combine like terms: -0.1428571429 + 4 = 3.8571428571 4 + -4x + x2 = 3.8571428571 Factor a perfect square on the left side: (x + -2)(x + -2) = 3.8571428571 Calculate the square root of the right side: 1.963961012 Break this problem into two subproblems by setting (x + -2) equal to 1.963961012 and -1.963961012.Subproblem 1
x + -2 = 1.963961012 Simplifying x + -2 = 1.963961012 Reorder the terms: -2 + x = 1.963961012 Solving -2 + x = 1.963961012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = 1.963961012 + 2 Combine like terms: -2 + 2 = 0 0 + x = 1.963961012 + 2 x = 1.963961012 + 2 Combine like terms: 1.963961012 + 2 = 3.963961012 x = 3.963961012 Simplifying x = 3.963961012Subproblem 2
x + -2 = -1.963961012 Simplifying x + -2 = -1.963961012 Reorder the terms: -2 + x = -1.963961012 Solving -2 + x = -1.963961012 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2' to each side of the equation. -2 + 2 + x = -1.963961012 + 2 Combine like terms: -2 + 2 = 0 0 + x = -1.963961012 + 2 x = -1.963961012 + 2 Combine like terms: -1.963961012 + 2 = 0.036038988 x = 0.036038988 Simplifying x = 0.036038988Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.963961012, 0.036038988}
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