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Simplifying (3x + -1)(3x + 4) = 8x Reorder the terms: (-1 + 3x)(3x + 4) = 8x Reorder the terms: (-1 + 3x)(4 + 3x) = 8x Multiply (-1 + 3x) * (4 + 3x) (-1(4 + 3x) + 3x * (4 + 3x)) = 8x ((4 * -1 + 3x * -1) + 3x * (4 + 3x)) = 8x ((-4 + -3x) + 3x * (4 + 3x)) = 8x (-4 + -3x + (4 * 3x + 3x * 3x)) = 8x (-4 + -3x + (12x + 9x2)) = 8x Combine like terms: -3x + 12x = 9x (-4 + 9x + 9x2) = 8x Solving -4 + 9x + 9x2 = 8x Solving for variable 'x'. Reorder the terms: -4 + 9x + -8x + 9x2 = 8x + -8x Combine like terms: 9x + -8x = 1x -4 + 1x + 9x2 = 8x + -8x Combine like terms: 8x + -8x = 0 -4 + 1x + 9x2 = 0 Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -0.4444444444 + 0.1111111111x + x2 = 0 Move the constant term to the right: Add '0.4444444444' to each side of the equation. -0.4444444444 + 0.1111111111x + 0.4444444444 + x2 = 0 + 0.4444444444 Reorder the terms: -0.4444444444 + 0.4444444444 + 0.1111111111x + x2 = 0 + 0.4444444444 Combine like terms: -0.4444444444 + 0.4444444444 = 0.0000000000 0.0000000000 + 0.1111111111x + x2 = 0 + 0.4444444444 0.1111111111x + x2 = 0 + 0.4444444444 Combine like terms: 0 + 0.4444444444 = 0.4444444444 0.1111111111x + x2 = 0.4444444444 The x term is 0.1111111111x. Take half its coefficient (0.05555555555). Square it (0.003086419752) and add it to both sides. Add '0.003086419752' to each side of the equation. 0.1111111111x + 0.003086419752 + x2 = 0.4444444444 + 0.003086419752 Reorder the terms: 0.003086419752 + 0.1111111111x + x2 = 0.4444444444 + 0.003086419752 Combine like terms: 0.4444444444 + 0.003086419752 = 0.447530864152 0.003086419752 + 0.1111111111x + x2 = 0.447530864152 Factor a perfect square on the left side: (x + 0.05555555555)(x + 0.05555555555) = 0.447530864152 Calculate the square root of the right side: 0.668977477 Break this problem into two subproblems by setting (x + 0.05555555555) equal to 0.668977477 and -0.668977477.Subproblem 1
x + 0.05555555555 = 0.668977477 Simplifying x + 0.05555555555 = 0.668977477 Reorder the terms: 0.05555555555 + x = 0.668977477 Solving 0.05555555555 + x = 0.668977477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = 0.668977477 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = 0.668977477 + -0.05555555555 x = 0.668977477 + -0.05555555555 Combine like terms: 0.668977477 + -0.05555555555 = 0.61342192145 x = 0.61342192145 Simplifying x = 0.61342192145Subproblem 2
x + 0.05555555555 = -0.668977477 Simplifying x + 0.05555555555 = -0.668977477 Reorder the terms: 0.05555555555 + x = -0.668977477 Solving 0.05555555555 + x = -0.668977477 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.05555555555' to each side of the equation. 0.05555555555 + -0.05555555555 + x = -0.668977477 + -0.05555555555 Combine like terms: 0.05555555555 + -0.05555555555 = 0.00000000000 0.00000000000 + x = -0.668977477 + -0.05555555555 x = -0.668977477 + -0.05555555555 Combine like terms: -0.668977477 + -0.05555555555 = -0.72453303255 x = -0.72453303255 Simplifying x = -0.72453303255Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.61342192145, -0.72453303255}
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