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Simplifying 7x(3x + -1) = 2 Reorder the terms: 7x(-1 + 3x) = 2 (-1 * 7x + 3x * 7x) = 2 (-7x + 21x2) = 2 Solving -7x + 21x2 = 2 Solving for variable 'x'. Reorder the terms: -2 + -7x + 21x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -2 + -7x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -0.09523809524 + -0.3333333333x + x2 = 0 Move the constant term to the right: Add '0.09523809524' to each side of the equation. -0.09523809524 + -0.3333333333x + 0.09523809524 + x2 = 0 + 0.09523809524 Reorder the terms: -0.09523809524 + 0.09523809524 + -0.3333333333x + x2 = 0 + 0.09523809524 Combine like terms: -0.09523809524 + 0.09523809524 = 0.00000000000 0.00000000000 + -0.3333333333x + x2 = 0 + 0.09523809524 -0.3333333333x + x2 = 0 + 0.09523809524 Combine like terms: 0 + 0.09523809524 = 0.09523809524 -0.3333333333x + x2 = 0.09523809524 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 = 0.09523809524 + 0.02777777779 Reorder the terms: 0.02777777779 + -0.3333333333x + x2 = 0.09523809524 + 0.02777777779 Combine like terms: 0.09523809524 + 0.02777777779 = 0.12301587303 0.02777777779 + -0.3333333333x + x2 = 0.12301587303 Factor a perfect square on the left side: (x + -0.1666666667)(x + -0.1666666667) = 0.12301587303 Calculate the square root of the right side: 0.350736187 Break this problem into two subproblems by setting (x + -0.1666666667) equal to 0.350736187 and -0.350736187.Subproblem 1
x + -0.1666666667 = 0.350736187 Simplifying x + -0.1666666667 = 0.350736187 Reorder the terms: -0.1666666667 + x = 0.350736187 Solving -0.1666666667 + x = 0.350736187 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 = 0.350736187 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = 0.350736187 + 0.1666666667 x = 0.350736187 + 0.1666666667 Combine like terms: 0.350736187 + 0.1666666667 = 0.5174028537 x = 0.5174028537 Simplifying x = 0.5174028537Subproblem 2
x + -0.1666666667 = -0.350736187 Simplifying x + -0.1666666667 = -0.350736187 Reorder the terms: -0.1666666667 + x = -0.350736187 Solving -0.1666666667 + x = -0.350736187 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 = -0.350736187 + 0.1666666667 Combine like terms: -0.1666666667 + 0.1666666667 = 0.0000000000 0.0000000000 + x = -0.350736187 + 0.1666666667 x = -0.350736187 + 0.1666666667 Combine like terms: -0.350736187 + 0.1666666667 = -0.1840695203 x = -0.1840695203 Simplifying x = -0.1840695203Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.5174028537, -0.1840695203}
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