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Simplifying (5x + -10)(5 + -1x) = -6 Reorder the terms: (-10 + 5x)(5 + -1x) = -6 Multiply (-10 + 5x) * (5 + -1x) (-10(5 + -1x) + 5x * (5 + -1x)) = -6 ((5 * -10 + -1x * -10) + 5x * (5 + -1x)) = -6 ((-50 + 10x) + 5x * (5 + -1x)) = -6 (-50 + 10x + (5 * 5x + -1x * 5x)) = -6 (-50 + 10x + (25x + -5x2)) = -6 Combine like terms: 10x + 25x = 35x (-50 + 35x + -5x2) = -6 Solving -50 + 35x + -5x2 = -6 Solving for variable 'x'. Reorder the terms: -50 + 6 + 35x + -5x2 = -6 + 6 Combine like terms: -50 + 6 = -44 -44 + 35x + -5x2 = -6 + 6 Combine like terms: -6 + 6 = 0 -44 + 35x + -5x2 = 0 Begin completing the square. Divide all terms by -5 the coefficient of the squared term: Divide each side by '-5'. 8.8 + -7x + x2 = 0 Move the constant term to the right: Add '-8.8' to each side of the equation. 8.8 + -7x + -8.8 + x2 = 0 + -8.8 Reorder the terms: 8.8 + -8.8 + -7x + x2 = 0 + -8.8 Combine like terms: 8.8 + -8.8 = 0.0 0.0 + -7x + x2 = 0 + -8.8 -7x + x2 = 0 + -8.8 Combine like terms: 0 + -8.8 = -8.8 -7x + x2 = -8.8 The x term is -7x. Take half its coefficient (-3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. -7x + 12.25 + x2 = -8.8 + 12.25 Reorder the terms: 12.25 + -7x + x2 = -8.8 + 12.25 Combine like terms: -8.8 + 12.25 = 3.45 12.25 + -7x + x2 = 3.45 Factor a perfect square on the left side: (x + -3.5)(x + -3.5) = 3.45 Calculate the square root of the right side: 1.857417562 Break this problem into two subproblems by setting (x + -3.5) equal to 1.857417562 and -1.857417562.Subproblem 1
x + -3.5 = 1.857417562 Simplifying x + -3.5 = 1.857417562 Reorder the terms: -3.5 + x = 1.857417562 Solving -3.5 + x = 1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = 1.857417562 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = 1.857417562 + 3.5 x = 1.857417562 + 3.5 Combine like terms: 1.857417562 + 3.5 = 5.357417562 x = 5.357417562 Simplifying x = 5.357417562Subproblem 2
x + -3.5 = -1.857417562 Simplifying x + -3.5 = -1.857417562 Reorder the terms: -3.5 + x = -1.857417562 Solving -3.5 + x = -1.857417562 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.5' to each side of the equation. -3.5 + 3.5 + x = -1.857417562 + 3.5 Combine like terms: -3.5 + 3.5 = 0.0 0.0 + x = -1.857417562 + 3.5 x = -1.857417562 + 3.5 Combine like terms: -1.857417562 + 3.5 = 1.642582438 x = 1.642582438 Simplifying x = 1.642582438Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.357417562, 1.642582438}
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