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Simplifying (5x + 4)(x + 3) = 2 Reorder the terms: (4 + 5x)(x + 3) = 2 Reorder the terms: (4 + 5x)(3 + x) = 2 Multiply (4 + 5x) * (3 + x) (4(3 + x) + 5x * (3 + x)) = 2 ((3 * 4 + x * 4) + 5x * (3 + x)) = 2 ((12 + 4x) + 5x * (3 + x)) = 2 (12 + 4x + (3 * 5x + x * 5x)) = 2 (12 + 4x + (15x + 5x2)) = 2 Combine like terms: 4x + 15x = 19x (12 + 19x + 5x2) = 2 Solving 12 + 19x + 5x2 = 2 Solving for variable 'x'. Reorder the terms: 12 + -2 + 19x + 5x2 = 2 + -2 Combine like terms: 12 + -2 = 10 10 + 19x + 5x2 = 2 + -2 Combine like terms: 2 + -2 = 0 10 + 19x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 2 + 3.8x + x2 = 0 Move the constant term to the right: Add '-2' to each side of the equation. 2 + 3.8x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3.8x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3.8x + x2 = 0 + -2 3.8x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3.8x + x2 = -2 The x term is 3.8x. Take half its coefficient (1.9). Square it (3.61) and add it to both sides. Add '3.61' to each side of the equation. 3.8x + 3.61 + x2 = -2 + 3.61 Reorder the terms: 3.61 + 3.8x + x2 = -2 + 3.61 Combine like terms: -2 + 3.61 = 1.61 3.61 + 3.8x + x2 = 1.61 Factor a perfect square on the left side: (x + 1.9)(x + 1.9) = 1.61 Calculate the square root of the right side: 1.268857754 Break this problem into two subproblems by setting (x + 1.9) equal to 1.268857754 and -1.268857754.Subproblem 1
x + 1.9 = 1.268857754 Simplifying x + 1.9 = 1.268857754 Reorder the terms: 1.9 + x = 1.268857754 Solving 1.9 + x = 1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = 1.268857754 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = 1.268857754 + -1.9 x = 1.268857754 + -1.9 Combine like terms: 1.268857754 + -1.9 = -0.631142246 x = -0.631142246 Simplifying x = -0.631142246Subproblem 2
x + 1.9 = -1.268857754 Simplifying x + 1.9 = -1.268857754 Reorder the terms: 1.9 + x = -1.268857754 Solving 1.9 + x = -1.268857754 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.9' to each side of the equation. 1.9 + -1.9 + x = -1.268857754 + -1.9 Combine like terms: 1.9 + -1.9 = 0.0 0.0 + x = -1.268857754 + -1.9 x = -1.268857754 + -1.9 Combine like terms: -1.268857754 + -1.9 = -3.168857754 x = -3.168857754 Simplifying x = -3.168857754Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.631142246, -3.168857754}
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