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Simplifying (7x + -10)(3x + 40) = 180 Reorder the terms: (-10 + 7x)(3x + 40) = 180 Reorder the terms: (-10 + 7x)(40 + 3x) = 180 Multiply (-10 + 7x) * (40 + 3x) (-10(40 + 3x) + 7x * (40 + 3x)) = 180 ((40 * -10 + 3x * -10) + 7x * (40 + 3x)) = 180 ((-400 + -30x) + 7x * (40 + 3x)) = 180 (-400 + -30x + (40 * 7x + 3x * 7x)) = 180 (-400 + -30x + (280x + 21x2)) = 180 Combine like terms: -30x + 280x = 250x (-400 + 250x + 21x2) = 180 Solving -400 + 250x + 21x2 = 180 Solving for variable 'x'. Reorder the terms: -400 + -180 + 250x + 21x2 = 180 + -180 Combine like terms: -400 + -180 = -580 -580 + 250x + 21x2 = 180 + -180 Combine like terms: 180 + -180 = 0 -580 + 250x + 21x2 = 0 Begin completing the square. Divide all terms by 21 the coefficient of the squared term: Divide each side by '21'. -27.61904762 + 11.9047619x + x2 = 0 Move the constant term to the right: Add '27.61904762' to each side of the equation. -27.61904762 + 11.9047619x + 27.61904762 + x2 = 0 + 27.61904762 Reorder the terms: -27.61904762 + 27.61904762 + 11.9047619x + x2 = 0 + 27.61904762 Combine like terms: -27.61904762 + 27.61904762 = 0.00000000 0.00000000 + 11.9047619x + x2 = 0 + 27.61904762 11.9047619x + x2 = 0 + 27.61904762 Combine like terms: 0 + 27.61904762 = 27.61904762 11.9047619x + x2 = 27.61904762 The x term is 11.9047619x. Take half its coefficient (5.95238095). Square it (35.43083897) and add it to both sides. Add '35.43083897' to each side of the equation. 11.9047619x + 35.43083897 + x2 = 27.61904762 + 35.43083897 Reorder the terms: 35.43083897 + 11.9047619x + x2 = 27.61904762 + 35.43083897 Combine like terms: 27.61904762 + 35.43083897 = 63.04988659 35.43083897 + 11.9047619x + x2 = 63.04988659 Factor a perfect square on the left side: (x + 5.95238095)(x + 5.95238095) = 63.04988659 Calculate the square root of the right side: 7.940395871 Break this problem into two subproblems by setting (x + 5.95238095) equal to 7.940395871 and -7.940395871.Subproblem 1
x + 5.95238095 = 7.940395871 Simplifying x + 5.95238095 = 7.940395871 Reorder the terms: 5.95238095 + x = 7.940395871 Solving 5.95238095 + x = 7.940395871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.95238095' to each side of the equation. 5.95238095 + -5.95238095 + x = 7.940395871 + -5.95238095 Combine like terms: 5.95238095 + -5.95238095 = 0.00000000 0.00000000 + x = 7.940395871 + -5.95238095 x = 7.940395871 + -5.95238095 Combine like terms: 7.940395871 + -5.95238095 = 1.988014921 x = 1.988014921 Simplifying x = 1.988014921Subproblem 2
x + 5.95238095 = -7.940395871 Simplifying x + 5.95238095 = -7.940395871 Reorder the terms: 5.95238095 + x = -7.940395871 Solving 5.95238095 + x = -7.940395871 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5.95238095' to each side of the equation. 5.95238095 + -5.95238095 + x = -7.940395871 + -5.95238095 Combine like terms: 5.95238095 + -5.95238095 = 0.00000000 0.00000000 + x = -7.940395871 + -5.95238095 x = -7.940395871 + -5.95238095 Combine like terms: -7.940395871 + -5.95238095 = -13.892776821 x = -13.892776821 Simplifying x = -13.892776821Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.988014921, -13.892776821}
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