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Simplifying 7x(6x + -1) = 2 Reorder the terms: 7x(-1 + 6x) = 2 (-1 * 7x + 6x * 7x) = 2 (-7x + 42x2) = 2 Solving -7x + 42x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -7x + 42x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -7x + 42x2 = 0 Begin completing the square. Divide all terms by 42 the coefficient of the squared term: Divide each side by '42'. -0.04761904762 + -0.1666666667x + x2 = 0 Move the constant term to the right: Add '0.04761904762' to each side of the equation. -0.04761904762 + -0.1666666667x + 0.04761904762 + x2 = 0 + 0.04761904762 Reorder the terms: -0.04761904762 + 0.04761904762 + -0.1666666667x + x2 = 0 + 0.04761904762 Combine like terms: -0.04761904762 + 0.04761904762 = 0.00000000000 0.00000000000 + -0.1666666667x + x2 = 0 + 0.04761904762 -0.1666666667x + x2 = 0 + 0.04761904762 Combine like terms: 0 + 0.04761904762 = 0.04761904762 -0.1666666667x + x2 = 0.04761904762 The x term is -0.1666666667x. Take half its coefficient (-0.08333333335). Square it (0.006944444447) and add it to both sides. Add '0.006944444447' to each side of the equation. -0.1666666667x + 0.006944444447 + x2 = 0.04761904762 + 0.006944444447 Reorder the terms: 0.006944444447 + -0.1666666667x + x2 = 0.04761904762 + 0.006944444447 Combine like terms: 0.04761904762 + 0.006944444447 = 0.054563492067 0.006944444447 + -0.1666666667x + x2 = 0.054563492067 Factor a perfect square on the left side: (x + -0.08333333335)(x + -0.08333333335) = 0.054563492067 Calculate the square root of the right side: 0.233588296 Break this problem into two subproblems by setting (x + -0.08333333335) equal to 0.233588296 and -0.233588296.Subproblem 1
x + -0.08333333335 = 0.233588296 Simplifying x + -0.08333333335 = 0.233588296 Reorder the terms: -0.08333333335 + x = 0.233588296 Solving -0.08333333335 + x = 0.233588296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = 0.233588296 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = 0.233588296 + 0.08333333335 x = 0.233588296 + 0.08333333335 Combine like terms: 0.233588296 + 0.08333333335 = 0.31692162935 x = 0.31692162935 Simplifying x = 0.31692162935Subproblem 2
x + -0.08333333335 = -0.233588296 Simplifying x + -0.08333333335 = -0.233588296 Reorder the terms: -0.08333333335 + x = -0.233588296 Solving -0.08333333335 + x = -0.233588296 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.08333333335' to each side of the equation. -0.08333333335 + 0.08333333335 + x = -0.233588296 + 0.08333333335 Combine like terms: -0.08333333335 + 0.08333333335 = 0.00000000000 0.00000000000 + x = -0.233588296 + 0.08333333335 x = -0.233588296 + 0.08333333335 Combine like terms: -0.233588296 + 0.08333333335 = -0.15025496265 x = -0.15025496265 Simplifying x = -0.15025496265Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.31692162935, -0.15025496265}
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