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Simplifying (5x + 6)(7x + 10) + -12x = 13x Reorder the terms: (6 + 5x)(7x + 10) + -12x = 13x Reorder the terms: (6 + 5x)(10 + 7x) + -12x = 13x Multiply (6 + 5x) * (10 + 7x) (6(10 + 7x) + 5x * (10 + 7x)) + -12x = 13x ((10 * 6 + 7x * 6) + 5x * (10 + 7x)) + -12x = 13x ((60 + 42x) + 5x * (10 + 7x)) + -12x = 13x (60 + 42x + (10 * 5x + 7x * 5x)) + -12x = 13x (60 + 42x + (50x + 35x2)) + -12x = 13x Combine like terms: 42x + 50x = 92x (60 + 92x + 35x2) + -12x = 13x Reorder the terms: 60 + 92x + -12x + 35x2 = 13x Combine like terms: 92x + -12x = 80x 60 + 80x + 35x2 = 13x Solving 60 + 80x + 35x2 = 13x Solving for variable 'x'. Reorder the terms: 60 + 80x + -13x + 35x2 = 13x + -13x Combine like terms: 80x + -13x = 67x 60 + 67x + 35x2 = 13x + -13x Combine like terms: 13x + -13x = 0 60 + 67x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. 1.714285714 + 1.914285714x + x2 = 0 Move the constant term to the right: Add '-1.714285714' to each side of the equation. 1.714285714 + 1.914285714x + -1.714285714 + x2 = 0 + -1.714285714 Reorder the terms: 1.714285714 + -1.714285714 + 1.914285714x + x2 = 0 + -1.714285714 Combine like terms: 1.714285714 + -1.714285714 = 0.000000000 0.000000000 + 1.914285714x + x2 = 0 + -1.714285714 1.914285714x + x2 = 0 + -1.714285714 Combine like terms: 0 + -1.714285714 = -1.714285714 1.914285714x + x2 = -1.714285714 The x term is 1.914285714x. Take half its coefficient (0.957142857). Square it (0.9161224487) and add it to both sides. Add '0.9161224487' to each side of the equation. 1.914285714x + 0.9161224487 + x2 = -1.714285714 + 0.9161224487 Reorder the terms: 0.9161224487 + 1.914285714x + x2 = -1.714285714 + 0.9161224487 Combine like terms: -1.714285714 + 0.9161224487 = -0.7981632653 0.9161224487 + 1.914285714x + x2 = -0.7981632653 Factor a perfect square on the left side: (x + 0.957142857)(x + 0.957142857) = -0.7981632653 Can't calculate square root of the right side. The solution to this equation could not be determined.
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