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Simplifying (4x + -42)(x + 3) = 55 Reorder the terms: (-42 + 4x)(x + 3) = 55 Reorder the terms: (-42 + 4x)(3 + x) = 55 Multiply (-42 + 4x) * (3 + x) (-42(3 + x) + 4x * (3 + x)) = 55 ((3 * -42 + x * -42) + 4x * (3 + x)) = 55 ((-126 + -42x) + 4x * (3 + x)) = 55 (-126 + -42x + (3 * 4x + x * 4x)) = 55 (-126 + -42x + (12x + 4x2)) = 55 Combine like terms: -42x + 12x = -30x (-126 + -30x + 4x2) = 55 Solving -126 + -30x + 4x2 = 55 Solving for variable 'x'. Reorder the terms: -126 + -55 + -30x + 4x2 = 55 + -55 Combine like terms: -126 + -55 = -181 -181 + -30x + 4x2 = 55 + -55 Combine like terms: 55 + -55 = 0 -181 + -30x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -45.25 + -7.5x + x2 = 0 Move the constant term to the right: Add '45.25' to each side of the equation. -45.25 + -7.5x + 45.25 + x2 = 0 + 45.25 Reorder the terms: -45.25 + 45.25 + -7.5x + x2 = 0 + 45.25 Combine like terms: -45.25 + 45.25 = 0.00 0.00 + -7.5x + x2 = 0 + 45.25 -7.5x + x2 = 0 + 45.25 Combine like terms: 0 + 45.25 = 45.25 -7.5x + x2 = 45.25 The x term is -7.5x. Take half its coefficient (-3.75). Square it (14.0625) and add it to both sides. Add '14.0625' to each side of the equation. -7.5x + 14.0625 + x2 = 45.25 + 14.0625 Reorder the terms: 14.0625 + -7.5x + x2 = 45.25 + 14.0625 Combine like terms: 45.25 + 14.0625 = 59.3125 14.0625 + -7.5x + x2 = 59.3125 Factor a perfect square on the left side: (x + -3.75)(x + -3.75) = 59.3125 Calculate the square root of the right side: 7.7014609 Break this problem into two subproblems by setting (x + -3.75) equal to 7.7014609 and -7.7014609.Subproblem 1
x + -3.75 = 7.7014609 Simplifying x + -3.75 = 7.7014609 Reorder the terms: -3.75 + x = 7.7014609 Solving -3.75 + x = 7.7014609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = 7.7014609 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = 7.7014609 + 3.75 x = 7.7014609 + 3.75 Combine like terms: 7.7014609 + 3.75 = 11.4514609 x = 11.4514609 Simplifying x = 11.4514609Subproblem 2
x + -3.75 = -7.7014609 Simplifying x + -3.75 = -7.7014609 Reorder the terms: -3.75 + x = -7.7014609 Solving -3.75 + x = -7.7014609 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.75' to each side of the equation. -3.75 + 3.75 + x = -7.7014609 + 3.75 Combine like terms: -3.75 + 3.75 = 0.00 0.00 + x = -7.7014609 + 3.75 x = -7.7014609 + 3.75 Combine like terms: -7.7014609 + 3.75 = -3.9514609 x = -3.9514609 Simplifying x = -3.9514609Solution
The solution to the problem is based on the solutions from the subproblems. x = {11.4514609, -3.9514609}
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