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Simplifying 3x(4x + 10) = 7x + -6 Reorder the terms: 3x(10 + 4x) = 7x + -6 (10 * 3x + 4x * 3x) = 7x + -6 (30x + 12x2) = 7x + -6 Reorder the terms: 30x + 12x2 = -6 + 7x Solving 30x + 12x2 = -6 + 7x Solving for variable 'x'. Reorder the terms: 6 + 30x + -7x + 12x2 = -6 + 7x + 6 + -7x Combine like terms: 30x + -7x = 23x 6 + 23x + 12x2 = -6 + 7x + 6 + -7x Reorder the terms: 6 + 23x + 12x2 = -6 + 6 + 7x + -7x Combine like terms: -6 + 6 = 0 6 + 23x + 12x2 = 0 + 7x + -7x 6 + 23x + 12x2 = 7x + -7x Combine like terms: 7x + -7x = 0 6 + 23x + 12x2 = 0 Begin completing the square. Divide all terms by 12 the coefficient of the squared term: Divide each side by '12'. 0.5 + 1.916666667x + x2 = 0 Move the constant term to the right: Add '-0.5' to each side of the equation. 0.5 + 1.916666667x + -0.5 + x2 = 0 + -0.5 Reorder the terms: 0.5 + -0.5 + 1.916666667x + x2 = 0 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + 1.916666667x + x2 = 0 + -0.5 1.916666667x + x2 = 0 + -0.5 Combine like terms: 0 + -0.5 = -0.5 1.916666667x + x2 = -0.5 The x term is 1.916666667x. Take half its coefficient (0.9583333335). Square it (0.9184027781) and add it to both sides. Add '0.9184027781' to each side of the equation. 1.916666667x + 0.9184027781 + x2 = -0.5 + 0.9184027781 Reorder the terms: 0.9184027781 + 1.916666667x + x2 = -0.5 + 0.9184027781 Combine like terms: -0.5 + 0.9184027781 = 0.4184027781 0.9184027781 + 1.916666667x + x2 = 0.4184027781 Factor a perfect square on the left side: (x + 0.9583333335)(x + 0.9583333335) = 0.4184027781 Calculate the square root of the right side: 0.646840613 Break this problem into two subproblems by setting (x + 0.9583333335) equal to 0.646840613 and -0.646840613.Subproblem 1
x + 0.9583333335 = 0.646840613 Simplifying x + 0.9583333335 = 0.646840613 Reorder the terms: 0.9583333335 + x = 0.646840613 Solving 0.9583333335 + x = 0.646840613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = 0.646840613 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = 0.646840613 + -0.9583333335 x = 0.646840613 + -0.9583333335 Combine like terms: 0.646840613 + -0.9583333335 = -0.3114927205 x = -0.3114927205 Simplifying x = -0.3114927205Subproblem 2
x + 0.9583333335 = -0.646840613 Simplifying x + 0.9583333335 = -0.646840613 Reorder the terms: 0.9583333335 + x = -0.646840613 Solving 0.9583333335 + x = -0.646840613 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9583333335' to each side of the equation. 0.9583333335 + -0.9583333335 + x = -0.646840613 + -0.9583333335 Combine like terms: 0.9583333335 + -0.9583333335 = 0.0000000000 0.0000000000 + x = -0.646840613 + -0.9583333335 x = -0.646840613 + -0.9583333335 Combine like terms: -0.646840613 + -0.9583333335 = -1.6051739465 x = -1.6051739465 Simplifying x = -1.6051739465Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.3114927205, -1.6051739465}
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