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Simplifying 42x2 + 14x + 1 = 0 Reorder the terms: 1 + 14x + 42x2 = 0 Solving 1 + 14x + 42x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. 0.02380952381 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '-0.02380952381' to each side of the equation. 0.02380952381 + 0.3333333333x + -0.02380952381 + x2 = 0 + -0.02380952381 Reorder the terms: 0.02380952381 + -0.02380952381 + 0.3333333333x + x2 = 0 + -0.02380952381 Combine like terms: 0.02380952381 + -0.02380952381 = 0.00000000000 0.00000000000 + 0.3333333333x + x2 = 0 + -0.02380952381 0.3333333333x + x2 = 0 + -0.02380952381 Combine like terms: 0 + -0.02380952381 = -0.02380952381 0.3333333333x + x2 = -0.02380952381 The x term is 0.3333333333x. Take half its coefficient (0.1666666667). Square it (0.02777777779) and add it to both sides. Add '0.02777777779' to each side of the equation. 0.3333333333x + 0.02777777779 + x2 = -0.02380952381 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = -0.02380952381 + 0.02777777779 Combine like terms: -0.02380952381 + 0.02777777779 = 0.00396825398 0.02777777779 + 0.3333333333x + x2 = 0.00396825398 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 0.00396825398 Calculate the square root of the right side: 0.062994079 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 0.062994079 and -0.062994079.Subproblem 1
x + 0.1666666667 = 0.062994079 Simplifying x + 0.1666666667 = 0.062994079 Reorder the terms: 0.1666666667 + x = 0.062994079 Solving 0.1666666667 + x = 0.062994079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = 0.062994079 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 0.062994079 + -0.1666666667 x = 0.062994079 + -0.1666666667 Combine like terms: 0.062994079 + -0.1666666667 = -0.1036725877 x = -0.1036725877 Simplifying x = -0.1036725877Subproblem 2
x + 0.1666666667 = -0.062994079 Simplifying x + 0.1666666667 = -0.062994079 Reorder the terms: 0.1666666667 + x = -0.062994079 Solving 0.1666666667 + x = -0.062994079 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.1666666667' to each side of the equation. 0.1666666667 + -0.1666666667 + x = -0.062994079 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -0.062994079 + -0.1666666667 x = -0.062994079 + -0.1666666667 Combine like terms: -0.062994079 + -0.1666666667 = -0.2296607457 x = -0.2296607457 Simplifying x = -0.2296607457Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.1036725877, -0.2296607457}
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