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Simplifying (7x + -3)(x + 6) = -2 Reorder the terms: (-3 + 7x)(x + 6) = -2 Reorder the terms: (-3 + 7x)(6 + x) = -2 Multiply (-3 + 7x) * (6 + x) (-3(6 + x) + 7x * (6 + x)) = -2 ((6 * -3 + x * -3) + 7x * (6 + x)) = -2 ((-18 + -3x) + 7x * (6 + x)) = -2 (-18 + -3x + (6 * 7x + x * 7x)) = -2 (-18 + -3x + (42x + 7x2)) = -2 Combine like terms: -3x + 42x = 39x (-18 + 39x + 7x2) = -2 Solving -18 + 39x + 7x2 = -2 Solving for variable 'x'. Reorder the terms: -18 + 2 + 39x + 7x2 = -2 + 2 Combine like terms: -18 + 2 = -16 -16 + 39x + 7x2 = -2 + 2 Combine like terms: -2 + 2 = 0 -16 + 39x + 7x2 = 0 Begin completing the square. Divide all terms by 7 the coefficient of the squared term: Divide each side by '7'. -2.285714286 + 5.571428571x + x2 = 0 Move the constant term to the right: Add '2.285714286' to each side of the equation. -2.285714286 + 5.571428571x + 2.285714286 + x2 = 0 + 2.285714286 Reorder the terms: -2.285714286 + 2.285714286 + 5.571428571x + x2 = 0 + 2.285714286 Combine like terms: -2.285714286 + 2.285714286 = 0.000000000 0.000000000 + 5.571428571x + x2 = 0 + 2.285714286 5.571428571x + x2 = 0 + 2.285714286 Combine like terms: 0 + 2.285714286 = 2.285714286 5.571428571x + x2 = 2.285714286 The x term is 5.571428571x. Take half its coefficient (2.785714286). Square it (7.760204083) and add it to both sides. Add '7.760204083' to each side of the equation. 5.571428571x + 7.760204083 + x2 = 2.285714286 + 7.760204083 Reorder the terms: 7.760204083 + 5.571428571x + x2 = 2.285714286 + 7.760204083 Combine like terms: 2.285714286 + 7.760204083 = 10.045918369 7.760204083 + 5.571428571x + x2 = 10.045918369 Factor a perfect square on the left side: (x + 2.785714286)(x + 2.785714286) = 10.045918369 Calculate the square root of the right side: 3.169529676 Break this problem into two subproblems by setting (x + 2.785714286) equal to 3.169529676 and -3.169529676.Subproblem 1
x + 2.785714286 = 3.169529676 Simplifying x + 2.785714286 = 3.169529676 Reorder the terms: 2.785714286 + x = 3.169529676 Solving 2.785714286 + x = 3.169529676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = 3.169529676 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = 3.169529676 + -2.785714286 x = 3.169529676 + -2.785714286 Combine like terms: 3.169529676 + -2.785714286 = 0.38381539 x = 0.38381539 Simplifying x = 0.38381539Subproblem 2
x + 2.785714286 = -3.169529676 Simplifying x + 2.785714286 = -3.169529676 Reorder the terms: 2.785714286 + x = -3.169529676 Solving 2.785714286 + x = -3.169529676 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.785714286' to each side of the equation. 2.785714286 + -2.785714286 + x = -3.169529676 + -2.785714286 Combine like terms: 2.785714286 + -2.785714286 = 0.000000000 0.000000000 + x = -3.169529676 + -2.785714286 x = -3.169529676 + -2.785714286 Combine like terms: -3.169529676 + -2.785714286 = -5.955243962 x = -5.955243962 Simplifying x = -5.955243962Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.38381539, -5.955243962}
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