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Simplifying (5x + 4)(x + 1) = 2 Reorder the terms: (4 + 5x)(x + 1) = 2 Reorder the terms: (4 + 5x)(1 + x) = 2 Multiply (4 + 5x) * (1 + x) (4(1 + x) + 5x * (1 + x)) = 2 ((1 * 4 + x * 4) + 5x * (1 + x)) = 2 ((4 + 4x) + 5x * (1 + x)) = 2 (4 + 4x + (1 * 5x + x * 5x)) = 2 (4 + 4x + (5x + 5x2)) = 2 Combine like terms: 4x + 5x = 9x (4 + 9x + 5x2) = 2 Solving 4 + 9x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: 4 + -2 + 9x + 5x2 = 2 + -2 Combine like terms: 4 + -2 = 2 2 + 9x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 2 + 9x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 0.4 + 1.8x + x2 = 0 Move the constant term to the right: Add '-0.4' to each side of the equation. 0.4 + 1.8x + -0.4 + x2 = 0 + -0.4 Reorder the terms: 0.4 + -0.4 + 1.8x + x2 = 0 + -0.4 Combine like terms: 0.4 + -0.4 = 0.0 0.0 + 1.8x + x2 = 0 + -0.4 1.8x + x2 = 0 + -0.4 Combine like terms: 0 + -0.4 = -0.4 1.8x + x2 = -0.4 The x term is 1.8x. Take half its coefficient (0.9). Square it (0.81) and add it to both sides. Add '0.81' to each side of the equation. 1.8x + 0.81 + x2 = -0.4 + 0.81 Reorder the terms: 0.81 + 1.8x + x2 = -0.4 + 0.81 Combine like terms: -0.4 + 0.81 = 0.41 0.81 + 1.8x + x2 = 0.41 Factor a perfect square on the left side: (x + 0.9)(x + 0.9) = 0.41 Calculate the square root of the right side: 0.640312424 Break this problem into two subproblems by setting (x + 0.9) equal to 0.640312424 and -0.640312424.Subproblem 1
x + 0.9 = 0.640312424 Simplifying x + 0.9 = 0.640312424 Reorder the terms: 0.9 + x = 0.640312424 Solving 0.9 + x = 0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = 0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = 0.640312424 + -0.9 x = 0.640312424 + -0.9 Combine like terms: 0.640312424 + -0.9 = -0.259687576 x = -0.259687576 Simplifying x = -0.259687576Subproblem 2
x + 0.9 = -0.640312424 Simplifying x + 0.9 = -0.640312424 Reorder the terms: 0.9 + x = -0.640312424 Solving 0.9 + x = -0.640312424 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9' to each side of the equation. 0.9 + -0.9 + x = -0.640312424 + -0.9 Combine like terms: 0.9 + -0.9 = 0.0 0.0 + x = -0.640312424 + -0.9 x = -0.640312424 + -0.9 Combine like terms: -0.640312424 + -0.9 = -1.540312424 x = -1.540312424 Simplifying x = -1.540312424Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.259687576, -1.540312424}
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