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Simplifying (3x + -2)(5x + 7) = (4 + -5x) Reorder the terms: (-2 + 3x)(5x + 7) = (4 + -5x) Reorder the terms: (-2 + 3x)(7 + 5x) = (4 + -5x) Multiply (-2 + 3x) * (7 + 5x) (-2(7 + 5x) + 3x * (7 + 5x)) = (4 + -5x) ((7 * -2 + 5x * -2) + 3x * (7 + 5x)) = (4 + -5x) ((-14 + -10x) + 3x * (7 + 5x)) = (4 + -5x) (-14 + -10x + (7 * 3x + 5x * 3x)) = (4 + -5x) (-14 + -10x + (21x + 15x2)) = (4 + -5x) Combine like terms: -10x + 21x = 11x (-14 + 11x + 15x2) = (4 + -5x) Remove parenthesis around (4 + -5x) -14 + 11x + 15x2 = 4 + -5x Solving -14 + 11x + 15x2 = 4 + -5x Solving for variable 'x'. Reorder the terms: -14 + -4 + 11x + 5x + 15x2 = 4 + -5x + -4 + 5x Combine like terms: -14 + -4 = -18 -18 + 11x + 5x + 15x2 = 4 + -5x + -4 + 5x Combine like terms: 11x + 5x = 16x -18 + 16x + 15x2 = 4 + -5x + -4 + 5x Reorder the terms: -18 + 16x + 15x2 = 4 + -4 + -5x + 5x Combine like terms: 4 + -4 = 0 -18 + 16x + 15x2 = 0 + -5x + 5x -18 + 16x + 15x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -18 + 16x + 15x2 = 0 Begin completing the square. Divide all terms by 15 the coefficient of the squared term: Divide each side by '15'. -1.2 + 1.066666667x + x2 = 0 Move the constant term to the right: Add '1.2' to each side of the equation. -1.2 + 1.066666667x + 1.2 + x2 = 0 + 1.2 Reorder the terms: -1.2 + 1.2 + 1.066666667x + x2 = 0 + 1.2 Combine like terms: -1.2 + 1.2 = 0.0 0.0 + 1.066666667x + x2 = 0 + 1.2 1.066666667x + x2 = 0 + 1.2 Combine like terms: 0 + 1.2 = 1.2 1.066666667x + x2 = 1.2 The x term is 1.066666667x. Take half its coefficient (0.5333333335). Square it (0.2844444446) and add it to both sides. Add '0.2844444446' to each side of the equation. 1.066666667x + 0.2844444446 + x2 = 1.2 + 0.2844444446 Reorder the terms: 0.2844444446 + 1.066666667x + x2 = 1.2 + 0.2844444446 Combine like terms: 1.2 + 0.2844444446 = 1.4844444446 0.2844444446 + 1.066666667x + x2 = 1.4844444446 Factor a perfect square on the left side: (x + 0.5333333335)(x + 0.5333333335) = 1.4844444446 Calculate the square root of the right side: 1.218377792 Break this problem into two subproblems by setting (x + 0.5333333335) equal to 1.218377792 and -1.218377792.Subproblem 1
x + 0.5333333335 = 1.218377792 Simplifying x + 0.5333333335 = 1.218377792 Reorder the terms: 0.5333333335 + x = 1.218377792 Solving 0.5333333335 + x = 1.218377792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = 1.218377792 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = 1.218377792 + -0.5333333335 x = 1.218377792 + -0.5333333335 Combine like terms: 1.218377792 + -0.5333333335 = 0.6850444585 x = 0.6850444585 Simplifying x = 0.6850444585Subproblem 2
x + 0.5333333335 = -1.218377792 Simplifying x + 0.5333333335 = -1.218377792 Reorder the terms: 0.5333333335 + x = -1.218377792 Solving 0.5333333335 + x = -1.218377792 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5333333335' to each side of the equation. 0.5333333335 + -0.5333333335 + x = -1.218377792 + -0.5333333335 Combine like terms: 0.5333333335 + -0.5333333335 = 0.0000000000 0.0000000000 + x = -1.218377792 + -0.5333333335 x = -1.218377792 + -0.5333333335 Combine like terms: -1.218377792 + -0.5333333335 = -1.7517111255 x = -1.7517111255 Simplifying x = -1.7517111255Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.6850444585, -1.7517111255}
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