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Simplifying (5x + 6)(2x + 9) = x Reorder the terms: (6 + 5x)(2x + 9) = x Reorder the terms: (6 + 5x)(9 + 2x) = x Multiply (6 + 5x) * (9 + 2x) (6(9 + 2x) + 5x * (9 + 2x)) = x ((9 * 6 + 2x * 6) + 5x * (9 + 2x)) = x ((54 + 12x) + 5x * (9 + 2x)) = x (54 + 12x + (9 * 5x + 2x * 5x)) = x (54 + 12x + (45x + 10x2)) = x Combine like terms: 12x + 45x = 57x (54 + 57x + 10x2) = x Solving 54 + 57x + 10x2 = x Solving for variable 'x'. Reorder the terms: 54 + 57x + -1x + 10x2 = x + -1x Combine like terms: 57x + -1x = 56x 54 + 56x + 10x2 = x + -1x Combine like terms: x + -1x = 0 54 + 56x + 10x2 = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(27 + 28x + 5x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(27 + 28x + 5x2)' equal to zero and attempt to solve: Simplifying 27 + 28x + 5x2 = 0 Solving 27 + 28x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 5.4 + 5.6x + x2 = 0 Move the constant term to the right: Add '-5.4' to each side of the equation. 5.4 + 5.6x + -5.4 + x2 = 0 + -5.4 Reorder the terms: 5.4 + -5.4 + 5.6x + x2 = 0 + -5.4 Combine like terms: 5.4 + -5.4 = 0.0 0.0 + 5.6x + x2 = 0 + -5.4 5.6x + x2 = 0 + -5.4 Combine like terms: 0 + -5.4 = -5.4 5.6x + x2 = -5.4 The x term is 5.6x. Take half its coefficient (2.8). Square it (7.84) and add it to both sides. Add '7.84' to each side of the equation. 5.6x + 7.84 + x2 = -5.4 + 7.84 Reorder the terms: 7.84 + 5.6x + x2 = -5.4 + 7.84 Combine like terms: -5.4 + 7.84 = 2.44 7.84 + 5.6x + x2 = 2.44 Factor a perfect square on the left side: (x + 2.8)(x + 2.8) = 2.44 Calculate the square root of the right side: 1.562049935 Break this problem into two subproblems by setting (x + 2.8) equal to 1.562049935 and -1.562049935.Subproblem 1
x + 2.8 = 1.562049935 Simplifying x + 2.8 = 1.562049935 Reorder the terms: 2.8 + x = 1.562049935 Solving 2.8 + x = 1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = 1.562049935 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = 1.562049935 + -2.8 x = 1.562049935 + -2.8 Combine like terms: 1.562049935 + -2.8 = -1.237950065 x = -1.237950065 Simplifying x = -1.237950065Subproblem 2
x + 2.8 = -1.562049935 Simplifying x + 2.8 = -1.562049935 Reorder the terms: 2.8 + x = -1.562049935 Solving 2.8 + x = -1.562049935 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.8' to each side of the equation. 2.8 + -2.8 + x = -1.562049935 + -2.8 Combine like terms: 2.8 + -2.8 = 0.0 0.0 + x = -1.562049935 + -2.8 x = -1.562049935 + -2.8 Combine like terms: -1.562049935 + -2.8 = -4.362049935 x = -4.362049935 Simplifying x = -4.362049935Solution
The solution to the problem is based on the solutions from the subproblems. x = {-1.237950065, -4.362049935}Solution
x = {-1.237950065, -4.362049935}
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