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Simplifying (7x + -25)(4x + 5) = 180 Reorder the terms: (-25 + 7x)(4x + 5) = 180 Reorder the terms: (-25 + 7x)(5 + 4x) = 180 Multiply (-25 + 7x) * (5 + 4x) (-25(5 + 4x) + 7x * (5 + 4x)) = 180 ((5 * -25 + 4x * -25) + 7x * (5 + 4x)) = 180 ((-125 + -100x) + 7x * (5 + 4x)) = 180 (-125 + -100x + (5 * 7x + 4x * 7x)) = 180 (-125 + -100x + (35x + 28x2)) = 180 Combine like terms: -100x + 35x = -65x (-125 + -65x + 28x2) = 180 Solving -125 + -65x + 28x2 = 180 Solving for variable 'x'. Reorder the terms: -125 + -180 + -65x + 28x2 = 180 + -180 Combine like terms: -125 + -180 = -305 -305 + -65x + 28x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -305 + -65x + 28x2 = 0 Begin completing the square. Divide all terms by 28 the coefficient of the squared term: Divide each side by '28'. -10.89285714 + -2.321428571x + x2 = 0 Move the constant term to the right: Add '10.89285714' to each side of the equation. -10.89285714 + -2.321428571x + 10.89285714 + x2 = 0 + 10.89285714 Reorder the terms: -10.89285714 + 10.89285714 + -2.321428571x + x2 = 0 + 10.89285714 Combine like terms: -10.89285714 + 10.89285714 = 0.00000000 0.00000000 + -2.321428571x + x2 = 0 + 10.89285714 -2.321428571x + x2 = 0 + 10.89285714 Combine like terms: 0 + 10.89285714 = 10.89285714 -2.321428571x + x2 = 10.89285714 The x term is -2.321428571x. Take half its coefficient (-1.160714286). Square it (1.347257654) and add it to both sides. Add '1.347257654' to each side of the equation. -2.321428571x + 1.347257654 + x2 = 10.89285714 + 1.347257654 Reorder the terms: 1.347257654 + -2.321428571x + x2 = 10.89285714 + 1.347257654 Combine like terms: 10.89285714 + 1.347257654 = 12.240114794 1.347257654 + -2.321428571x + x2 = 12.240114794 Factor a perfect square on the left side: (x + -1.160714286)(x + -1.160714286) = 12.240114794 Calculate the square root of the right side: 3.498587543 Break this problem into two subproblems by setting (x + -1.160714286) equal to 3.498587543 and -3.498587543.Subproblem 1
x + -1.160714286 = 3.498587543 Simplifying x + -1.160714286 = 3.498587543 Reorder the terms: -1.160714286 + x = 3.498587543 Solving -1.160714286 + x = 3.498587543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.160714286' to each side of the equation. -1.160714286 + 1.160714286 + x = 3.498587543 + 1.160714286 Combine like terms: -1.160714286 + 1.160714286 = 0.000000000 0.000000000 + x = 3.498587543 + 1.160714286 x = 3.498587543 + 1.160714286 Combine like terms: 3.498587543 + 1.160714286 = 4.659301829 x = 4.659301829 Simplifying x = 4.659301829Subproblem 2
x + -1.160714286 = -3.498587543 Simplifying x + -1.160714286 = -3.498587543 Reorder the terms: -1.160714286 + x = -3.498587543 Solving -1.160714286 + x = -3.498587543 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.160714286' to each side of the equation. -1.160714286 + 1.160714286 + x = -3.498587543 + 1.160714286 Combine like terms: -1.160714286 + 1.160714286 = 0.000000000 0.000000000 + x = -3.498587543 + 1.160714286 x = -3.498587543 + 1.160714286 Combine like terms: -3.498587543 + 1.160714286 = -2.337873257 x = -2.337873257 Simplifying x = -2.337873257Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.659301829, -2.337873257}
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