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Simplifying (7x + -34)(5x + 20) = 180 Reorder the terms: (-34 + 7x)(5x + 20) = 180 Reorder the terms: (-34 + 7x)(20 + 5x) = 180 Multiply (-34 + 7x) * (20 + 5x) (-34(20 + 5x) + 7x * (20 + 5x)) = 180 ((20 * -34 + 5x * -34) + 7x * (20 + 5x)) = 180 ((-680 + -170x) + 7x * (20 + 5x)) = 180 (-680 + -170x + (20 * 7x + 5x * 7x)) = 180 (-680 + -170x + (140x + 35x2)) = 180 Combine like terms: -170x + 140x = -30x (-680 + -30x + 35x2) = 180 Solving -680 + -30x + 35x2 = 180 Solving for variable 'x'. Reorder the terms: -680 + -180 + -30x + 35x2 = 180 + -180 Combine like terms: -680 + -180 = -860 -860 + -30x + 35x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -860 + -30x + 35x2 = 0 Factor out the Greatest Common Factor (GCF), '5'. 5(-172 + -6x + 7x2) = 0 Ignore the factor 5.Subproblem 1
Set the factor '(-172 + -6x + 7x2)' equal to zero and attempt to solve: Simplifying -172 + -6x + 7x2 = 0 Solving -172 + -6x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -24.57142857 + -0.8571428571x + x2 = 0 Move the constant term to the right: Add '24.57142857' to each side of the equation. -24.57142857 + -0.8571428571x + 24.57142857 + x2 = 0 + 24.57142857 Reorder the terms: -24.57142857 + 24.57142857 + -0.8571428571x + x2 = 0 + 24.57142857 Combine like terms: -24.57142857 + 24.57142857 = 0.00000000 0.00000000 + -0.8571428571x + x2 = 0 + 24.57142857 -0.8571428571x + x2 = 0 + 24.57142857 Combine like terms: 0 + 24.57142857 = 24.57142857 -0.8571428571x + x2 = 24.57142857 The x term is -0.8571428571x. Take half its coefficient (-0.4285714286). Square it (0.1836734694) and add it to both sides. Add '0.1836734694' to each side of the equation. -0.8571428571x + 0.1836734694 + x2 = 24.57142857 + 0.1836734694 Reorder the terms: 0.1836734694 + -0.8571428571x + x2 = 24.57142857 + 0.1836734694 Combine like terms: 24.57142857 + 0.1836734694 = 24.7551020394 0.1836734694 + -0.8571428571x + x2 = 24.7551020394 Factor a perfect square on the left side: (x + -0.4285714286)(x + -0.4285714286) = 24.7551020394 Calculate the square root of the right side: 4.975449933 Break this problem into two subproblems by setting (x + -0.4285714286) equal to 4.975449933 and -4.975449933.Subproblem 1
x + -0.4285714286 = 4.975449933 Simplifying x + -0.4285714286 = 4.975449933 Reorder the terms: -0.4285714286 + x = 4.975449933 Solving -0.4285714286 + x = 4.975449933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = 4.975449933 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = 4.975449933 + 0.4285714286 x = 4.975449933 + 0.4285714286 Combine like terms: 4.975449933 + 0.4285714286 = 5.4040213616 x = 5.4040213616 Simplifying x = 5.4040213616Subproblem 2
x + -0.4285714286 = -4.975449933 Simplifying x + -0.4285714286 = -4.975449933 Reorder the terms: -0.4285714286 + x = -4.975449933 Solving -0.4285714286 + x = -4.975449933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '0.4285714286' to each side of the equation. -0.4285714286 + 0.4285714286 + x = -4.975449933 + 0.4285714286 Combine like terms: -0.4285714286 + 0.4285714286 = 0.0000000000 0.0000000000 + x = -4.975449933 + 0.4285714286 x = -4.975449933 + 0.4285714286 Combine like terms: -4.975449933 + 0.4285714286 = -4.5468785044 x = -4.5468785044 Simplifying x = -4.5468785044Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.4040213616, -4.5468785044}Solution
x = {5.4040213616, -4.5468785044}
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