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Simplifying (6x + -1)(x + 5) = 7 Reorder the terms: (-1 + 6x)(x + 5) = 7 Reorder the terms: (-1 + 6x)(5 + x) = 7 Multiply (-1 + 6x) * (5 + x) (-1(5 + x) + 6x * (5 + x)) = 7 ((5 * -1 + x * -1) + 6x * (5 + x)) = 7 ((-5 + -1x) + 6x * (5 + x)) = 7 (-5 + -1x + (5 * 6x + x * 6x)) = 7 (-5 + -1x + (30x + 6x2)) = 7 Combine like terms: -1x + 30x = 29x (-5 + 29x + 6x2) = 7 Solving -5 + 29x + 6x2 = 7 Solving for variable 'x'. Reorder the terms: -5 + -7 + 29x + 6x2 = 7 + -7 Combine like terms: -5 + -7 = -12 -12 + 29x + 6x2 = 7 + -7 Combine like terms: 7 + -7 = 0 -12 + 29x + 6x2 = 0 Begin completing the square. Divide all terms by 6 the coefficient of the squared term: Divide each side by '6'. -2 + 4.833333333x + x2 = 0 Move the constant term to the right: Add '2' to each side of the equation. -2 + 4.833333333x + 2 + x2 = 0 + 2 Reorder the terms: -2 + 2 + 4.833333333x + x2 = 0 + 2 Combine like terms: -2 + 2 = 0 0 + 4.833333333x + x2 = 0 + 2 4.833333333x + x2 = 0 + 2 Combine like terms: 0 + 2 = 2 4.833333333x + x2 = 2 The x term is 4.833333333x. Take half its coefficient (2.416666667). Square it (5.840277779) and add it to both sides. Add '5.840277779' to each side of the equation. 4.833333333x + 5.840277779 + x2 = 2 + 5.840277779 Reorder the terms: 5.840277779 + 4.833333333x + x2 = 2 + 5.840277779 Combine like terms: 2 + 5.840277779 = 7.840277779 5.840277779 + 4.833333333x + x2 = 7.840277779 Factor a perfect square on the left side: (x + 2.416666667)(x + 2.416666667) = 7.840277779 Calculate the square root of the right side: 2.800049603 Break this problem into two subproblems by setting (x + 2.416666667) equal to 2.800049603 and -2.800049603.Subproblem 1
x + 2.416666667 = 2.800049603 Simplifying x + 2.416666667 = 2.800049603 Reorder the terms: 2.416666667 + x = 2.800049603 Solving 2.416666667 + x = 2.800049603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.416666667' to each side of the equation. 2.416666667 + -2.416666667 + x = 2.800049603 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = 2.800049603 + -2.416666667 x = 2.800049603 + -2.416666667 Combine like terms: 2.800049603 + -2.416666667 = 0.383382936 x = 0.383382936 Simplifying x = 0.383382936Subproblem 2
x + 2.416666667 = -2.800049603 Simplifying x + 2.416666667 = -2.800049603 Reorder the terms: 2.416666667 + x = -2.800049603 Solving 2.416666667 + x = -2.800049603 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.416666667' to each side of the equation. 2.416666667 + -2.416666667 + x = -2.800049603 + -2.416666667 Combine like terms: 2.416666667 + -2.416666667 = 0.000000000 0.000000000 + x = -2.800049603 + -2.416666667 x = -2.800049603 + -2.416666667 Combine like terms: -2.800049603 + -2.416666667 = -5.21671627 x = -5.21671627 Simplifying x = -5.21671627Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.383382936, -5.21671627}
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