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Simplifying (5x + -18)(4x + 7) = 180 Reorder the terms: (-18 + 5x)(4x + 7) = 180 Reorder the terms: (-18 + 5x)(7 + 4x) = 180 Multiply (-18 + 5x) * (7 + 4x) (-18(7 + 4x) + 5x * (7 + 4x)) = 180 ((7 * -18 + 4x * -18) + 5x * (7 + 4x)) = 180 ((-126 + -72x) + 5x * (7 + 4x)) = 180 (-126 + -72x + (7 * 5x + 4x * 5x)) = 180 (-126 + -72x + (35x + 20x2)) = 180 Combine like terms: -72x + 35x = -37x (-126 + -37x + 20x2) = 180 Solving -126 + -37x + 20x2 = 180 Solving for variable 'x'. Reorder the terms: -126 + -180 + -37x + 20x2 = 180 + -180 Combine like terms: -126 + -180 = -306 -306 + -37x + 20x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -306 + -37x + 20x2 = 0 Begin completing the square. Divide all terms by 20 the coefficient of the squared term: Divide each side by '20'. -15.3 + -1.85x + x2 = 0.0 Move the constant term to the right: Add '15.3' to each side of the equation. -15.3 + -1.85x + 15.3 + x2 = 0.0 + 15.3 Reorder the terms: -15.3 + 15.3 + -1.85x + x2 = 0.0 + 15.3 Combine like terms: -15.3 + 15.3 = 0.0 0.0 + -1.85x + x2 = 0.0 + 15.3 -1.85x + x2 = 0.0 + 15.3 Combine like terms: 0.0 + 15.3 = 15.3 -1.85x + x2 = 15.3 The x term is -1.85x. Take half its coefficient (-0.925). Square it (0.855625) and add it to both sides. Add '0.855625' to each side of the equation. -1.85x + 0.855625 + x2 = 15.3 + 0.855625 Reorder the terms: 0.855625 + -1.85x + x2 = 15.3 + 0.855625 Combine like terms: 15.3 + 0.855625 = 16.155625 0.855625 + -1.85x + x2 = 16.155625 Factor a perfect square on the left side: (x + -0.925)(x + -0.925) = 16.155625 Calculate the square root of the right side: 4.019406051 Break this problem into two subproblems by setting (x + -0.925) equal to 4.019406051 and -4.019406051.Subproblem 1
x + -0.925 = 4.019406051 Simplifying x + -0.925 = 4.019406051 Reorder the terms: -0.925 + x = 4.019406051 Solving -0.925 + x = 4.019406051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.925' to each side of the equation. -0.925 + 0.925 + x = 4.019406051 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + x = 4.019406051 + 0.925 x = 4.019406051 + 0.925 Combine like terms: 4.019406051 + 0.925 = 4.944406051 x = 4.944406051 Simplifying x = 4.944406051Subproblem 2
x + -0.925 = -4.019406051 Simplifying x + -0.925 = -4.019406051 Reorder the terms: -0.925 + x = -4.019406051 Solving -0.925 + x = -4.019406051 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.925' to each side of the equation. -0.925 + 0.925 + x = -4.019406051 + 0.925 Combine like terms: -0.925 + 0.925 = 0.000 0.000 + x = -4.019406051 + 0.925 x = -4.019406051 + 0.925 Combine like terms: -4.019406051 + 0.925 = -3.094406051 x = -3.094406051 Simplifying x = -3.094406051Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.944406051, -3.094406051}
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