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Simplifying x + 3x(7x + 2) = 46 Reorder the terms: x + 3x(2 + 7x) = 46 x + (2 * 3x + 7x * 3x) = 46 x + (6x + 21x2) = 46 Combine like terms: x + 6x = 7x 7x + 21x2 = 46 Solving 7x + 21x2 = 46 Solving for variable 'x'. Reorder the terms: -46 + 7x + 21x2 = 46 + -46 Combine like terms: 46 + -46 = 0 -46 + 7x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -2.19047619 + 0.3333333333x + x2 = 0 Move the constant term to the right: Add '2.19047619' to each side of the equation. -2.19047619 + 0.3333333333x + 2.19047619 + x2 = 0 + 2.19047619 Reorder the terms: -2.19047619 + 2.19047619 + 0.3333333333x + x2 = 0 + 2.19047619 Combine like terms: -2.19047619 + 2.19047619 = 0.00000000 0.00000000 + 0.3333333333x + x2 = 0 + 2.19047619 0.3333333333x + x2 = 0 + 2.19047619 Combine like terms: 0 + 2.19047619 = 2.19047619 0.3333333333x + x2 = 2.19047619 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 = 2.19047619 + 0.02777777779 Reorder the terms: 0.02777777779 + 0.3333333333x + x2 = 2.19047619 + 0.02777777779 Combine like terms: 2.19047619 + 0.02777777779 = 2.21825396779 0.02777777779 + 0.3333333333x + x2 = 2.21825396779 Factor a perfect square on the left side: (x + 0.1666666667)(x + 0.1666666667) = 2.21825396779 Calculate the square root of the right side: 1.489380397 Break this problem into two subproblems by setting (x + 0.1666666667) equal to 1.489380397 and -1.489380397.Subproblem 1
x + 0.1666666667 = 1.489380397 Simplifying x + 0.1666666667 = 1.489380397 Reorder the terms: 0.1666666667 + x = 1.489380397 Solving 0.1666666667 + x = 1.489380397 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 = 1.489380397 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = 1.489380397 + -0.1666666667 x = 1.489380397 + -0.1666666667 Combine like terms: 1.489380397 + -0.1666666667 = 1.3227137303 x = 1.3227137303 Simplifying x = 1.3227137303Subproblem 2
x + 0.1666666667 = -1.489380397 Simplifying x + 0.1666666667 = -1.489380397 Reorder the terms: 0.1666666667 + x = -1.489380397 Solving 0.1666666667 + x = -1.489380397 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 = -1.489380397 + -0.1666666667 Combine like terms: 0.1666666667 + -0.1666666667 = 0.0000000000 0.0000000000 + x = -1.489380397 + -0.1666666667 x = -1.489380397 + -0.1666666667 Combine like terms: -1.489380397 + -0.1666666667 = -1.6560470637 x = -1.6560470637 Simplifying x = -1.6560470637Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.3227137303, -1.6560470637}
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