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Simplifying (3x + -5)(x + 5) = 5 Reorder the terms: (-5 + 3x)(x + 5) = 5 Reorder the terms: (-5 + 3x)(5 + x) = 5 Multiply (-5 + 3x) * (5 + x) (-5(5 + x) + 3x * (5 + x)) = 5 ((5 * -5 + x * -5) + 3x * (5 + x)) = 5 ((-25 + -5x) + 3x * (5 + x)) = 5 (-25 + -5x + (5 * 3x + x * 3x)) = 5 (-25 + -5x + (15x + 3x2)) = 5 Combine like terms: -5x + 15x = 10x (-25 + 10x + 3x2) = 5 Solving -25 + 10x + 3x2 = 5 Solving for variable 'x'. Reorder the terms: -25 + -5 + 10x + 3x2 = 5 + -5 Combine like terms: -25 + -5 = -30 -30 + 10x + 3x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -30 + 10x + 3x2 = 0 Begin completing the square. Divide all terms by 3 the coefficient of the squared term: Divide each side by '3'. -10 + 3.333333333x + x2 = 0 Move the constant term to the right: Add '10' to each side of the equation. -10 + 3.333333333x + 10 + x2 = 0 + 10 Reorder the terms: -10 + 10 + 3.333333333x + x2 = 0 + 10 Combine like terms: -10 + 10 = 0 0 + 3.333333333x + x2 = 0 + 10 3.333333333x + x2 = 0 + 10 Combine like terms: 0 + 10 = 10 3.333333333x + x2 = 10 The x term is 3.333333333x. Take half its coefficient (1.666666667). Square it (2.777777779) and add it to both sides. Add '2.777777779' to each side of the equation. 3.333333333x + 2.777777779 + x2 = 10 + 2.777777779 Reorder the terms: 2.777777779 + 3.333333333x + x2 = 10 + 2.777777779 Combine like terms: 10 + 2.777777779 = 12.777777779 2.777777779 + 3.333333333x + x2 = 12.777777779 Factor a perfect square on the left side: (x + 1.666666667)(x + 1.666666667) = 12.777777779 Calculate the square root of the right side: 3.574601765 Break this problem into two subproblems by setting (x + 1.666666667) equal to 3.574601765 and -3.574601765.Subproblem 1
x + 1.666666667 = 3.574601765 Simplifying x + 1.666666667 = 3.574601765 Reorder the terms: 1.666666667 + x = 3.574601765 Solving 1.666666667 + x = 3.574601765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = 3.574601765 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = 3.574601765 + -1.666666667 x = 3.574601765 + -1.666666667 Combine like terms: 3.574601765 + -1.666666667 = 1.907935098 x = 1.907935098 Simplifying x = 1.907935098Subproblem 2
x + 1.666666667 = -3.574601765 Simplifying x + 1.666666667 = -3.574601765 Reorder the terms: 1.666666667 + x = -3.574601765 Solving 1.666666667 + x = -3.574601765 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.666666667' to each side of the equation. 1.666666667 + -1.666666667 + x = -3.574601765 + -1.666666667 Combine like terms: 1.666666667 + -1.666666667 = 0.000000000 0.000000000 + x = -3.574601765 + -1.666666667 x = -3.574601765 + -1.666666667 Combine like terms: -3.574601765 + -1.666666667 = -5.241268432 x = -5.241268432 Simplifying x = -5.241268432Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.907935098, -5.241268432}
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