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Simplifying (3x + -1)(3x + 7) + -1(2x + 5)(x) = 0 Reorder the terms: (-1 + 3x)(3x + 7) + -1(2x + 5)(x) = 0 Reorder the terms: (-1 + 3x)(7 + 3x) + -1(2x + 5)(x) = 0 Multiply (-1 + 3x) * (7 + 3x) (-1(7 + 3x) + 3x * (7 + 3x)) + -1(2x + 5)(x) = 0 ((7 * -1 + 3x * -1) + 3x * (7 + 3x)) + -1(2x + 5)(x) = 0 ((-7 + -3x) + 3x * (7 + 3x)) + -1(2x + 5)(x) = 0 (-7 + -3x + (7 * 3x + 3x * 3x)) + -1(2x + 5)(x) = 0 (-7 + -3x + (21x + 9x2)) + -1(2x + 5)(x) = 0 Combine like terms: -3x + 21x = 18x (-7 + 18x + 9x2) + -1(2x + 5)(x) = 0 Reorder the terms: -7 + 18x + 9x2 + -1(5 + 2x)(x) = 0 Reorder the terms for easier multiplication: -7 + 18x + 9x2 + -1x(5 + 2x) = 0 -7 + 18x + 9x2 + (5 * -1x + 2x * -1x) = 0 -7 + 18x + 9x2 + (-5x + -2x2) = 0 Reorder the terms: -7 + 18x + -5x + 9x2 + -2x2 = 0 Combine like terms: 18x + -5x = 13x -7 + 13x + 9x2 + -2x2 = 0 Combine like terms: 9x2 + -2x2 = 7x2 -7 + 13x + 7x2 = 0 Solving -7 + 13x + 7x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -1 + 1.857142857x + x2 = 0 Move the constant term to the right: Add '1' to each side of the equation. -1 + 1.857142857x + 1 + x2 = 0 + 1 Reorder the terms: -1 + 1 + 1.857142857x + x2 = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 1.857142857x + x2 = 0 + 1 1.857142857x + x2 = 0 + 1 Combine like terms: 0 + 1 = 1 1.857142857x + x2 = 1 The x term is 1.857142857x. Take half its coefficient (0.9285714285). Square it (0.8622448978) and add it to both sides. Add '0.8622448978' to each side of the equation. 1.857142857x + 0.8622448978 + x2 = 1 + 0.8622448978 Reorder the terms: 0.8622448978 + 1.857142857x + x2 = 1 + 0.8622448978 Combine like terms: 1 + 0.8622448978 = 1.8622448978 0.8622448978 + 1.857142857x + x2 = 1.8622448978 Factor a perfect square on the left side: (x + 0.9285714285)(x + 0.9285714285) = 1.8622448978 Calculate the square root of the right side: 1.364640941 Break this problem into two subproblems by setting (x + 0.9285714285) equal to 1.364640941 and -1.364640941.Subproblem 1
x + 0.9285714285 = 1.364640941 Simplifying x + 0.9285714285 = 1.364640941 Reorder the terms: 0.9285714285 + x = 1.364640941 Solving 0.9285714285 + x = 1.364640941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = 1.364640941 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = 1.364640941 + -0.9285714285 x = 1.364640941 + -0.9285714285 Combine like terms: 1.364640941 + -0.9285714285 = 0.4360695125 x = 0.4360695125 Simplifying x = 0.4360695125Subproblem 2
x + 0.9285714285 = -1.364640941 Simplifying x + 0.9285714285 = -1.364640941 Reorder the terms: 0.9285714285 + x = -1.364640941 Solving 0.9285714285 + x = -1.364640941 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9285714285' to each side of the equation. 0.9285714285 + -0.9285714285 + x = -1.364640941 + -0.9285714285 Combine like terms: 0.9285714285 + -0.9285714285 = 0.0000000000 0.0000000000 + x = -1.364640941 + -0.9285714285 x = -1.364640941 + -0.9285714285 Combine like terms: -1.364640941 + -0.9285714285 = -2.2932123695 x = -2.2932123695 Simplifying x = -2.2932123695Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.4360695125, -2.2932123695}
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