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Simplifying (7x + 4)(5x + 8) = 144 Reorder the terms: (4 + 7x)(5x + 8) = 144 Reorder the terms: (4 + 7x)(8 + 5x) = 144 Multiply (4 + 7x) * (8 + 5x) (4(8 + 5x) + 7x * (8 + 5x)) = 144 ((8 * 4 + 5x * 4) + 7x * (8 + 5x)) = 144 ((32 + 20x) + 7x * (8 + 5x)) = 144 (32 + 20x + (8 * 7x + 5x * 7x)) = 144 (32 + 20x + (56x + 35x2)) = 144 Combine like terms: 20x + 56x = 76x (32 + 76x + 35x2) = 144 Solving 32 + 76x + 35x2 = 144 Solving for variable 'x'. Reorder the terms: 32 + -144 + 76x + 35x2 = 144 + -144 Combine like terms: 32 + -144 = -112 -112 + 76x + 35x2 = 144 + -144 Combine like terms: 144 + -144 = 0 -112 + 76x + 35x2 = 0 Begin completing the square. Divide all terms by 35 the coefficient of the squared term: Divide each side by '35'. -3.2 + 2.171428571x + x2 = 0 Move the constant term to the right: Add '3.2' to each side of the equation. -3.2 + 2.171428571x + 3.2 + x2 = 0 + 3.2 Reorder the terms: -3.2 + 3.2 + 2.171428571x + x2 = 0 + 3.2 Combine like terms: -3.2 + 3.2 = 0.0 0.0 + 2.171428571x + x2 = 0 + 3.2 2.171428571x + x2 = 0 + 3.2 Combine like terms: 0 + 3.2 = 3.2 2.171428571x + x2 = 3.2 The x term is 2.171428571x. Take half its coefficient (1.085714286). Square it (1.178775511) and add it to both sides. Add '1.178775511' to each side of the equation. 2.171428571x + 1.178775511 + x2 = 3.2 + 1.178775511 Reorder the terms: 1.178775511 + 2.171428571x + x2 = 3.2 + 1.178775511 Combine like terms: 3.2 + 1.178775511 = 4.378775511 1.178775511 + 2.171428571x + x2 = 4.378775511 Factor a perfect square on the left side: (x + 1.085714286)(x + 1.085714286) = 4.378775511 Calculate the square root of the right side: 2.092552391 Break this problem into two subproblems by setting (x + 1.085714286) equal to 2.092552391 and -2.092552391.Subproblem 1
x + 1.085714286 = 2.092552391 Simplifying x + 1.085714286 = 2.092552391 Reorder the terms: 1.085714286 + x = 2.092552391 Solving 1.085714286 + x = 2.092552391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.085714286' to each side of the equation. 1.085714286 + -1.085714286 + x = 2.092552391 + -1.085714286 Combine like terms: 1.085714286 + -1.085714286 = 0.000000000 0.000000000 + x = 2.092552391 + -1.085714286 x = 2.092552391 + -1.085714286 Combine like terms: 2.092552391 + -1.085714286 = 1.006838105 x = 1.006838105 Simplifying x = 1.006838105Subproblem 2
x + 1.085714286 = -2.092552391 Simplifying x + 1.085714286 = -2.092552391 Reorder the terms: 1.085714286 + x = -2.092552391 Solving 1.085714286 + x = -2.092552391 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.085714286' to each side of the equation. 1.085714286 + -1.085714286 + x = -2.092552391 + -1.085714286 Combine like terms: 1.085714286 + -1.085714286 = 0.000000000 0.000000000 + x = -2.092552391 + -1.085714286 x = -2.092552391 + -1.085714286 Combine like terms: -2.092552391 + -1.085714286 = -3.178266677 x = -3.178266677 Simplifying x = -3.178266677Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.006838105, -3.178266677}
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