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Simplifying (5x + 5)(x + -5) = 7x Reorder the terms: (5 + 5x)(x + -5) = 7x Reorder the terms: (5 + 5x)(-5 + x) = 7x Multiply (5 + 5x) * (-5 + x) (5(-5 + x) + 5x * (-5 + x)) = 7x ((-5 * 5 + x * 5) + 5x * (-5 + x)) = 7x ((-25 + 5x) + 5x * (-5 + x)) = 7x (-25 + 5x + (-5 * 5x + x * 5x)) = 7x (-25 + 5x + (-25x + 5x2)) = 7x Combine like terms: 5x + -25x = -20x (-25 + -20x + 5x2) = 7x Solving -25 + -20x + 5x2 = 7x Solving for variable 'x'. Reorder the terms: -25 + -20x + -7x + 5x2 = 7x + -7x Combine like terms: -20x + -7x = -27x -25 + -27x + 5x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -25 + -27x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -5 + -5.4x + x2 = 0 Move the constant term to the right: Add '5' to each side of the equation. -5 + -5.4x + 5 + x2 = 0 + 5 Reorder the terms: -5 + 5 + -5.4x + x2 = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -5.4x + x2 = 0 + 5 -5.4x + x2 = 0 + 5 Combine like terms: 0 + 5 = 5 -5.4x + x2 = 5 The x term is -5.4x. Take half its coefficient (-2.7). Square it (7.29) and add it to both sides. Add '7.29' to each side of the equation. -5.4x + 7.29 + x2 = 5 + 7.29 Reorder the terms: 7.29 + -5.4x + x2 = 5 + 7.29 Combine like terms: 5 + 7.29 = 12.29 7.29 + -5.4x + x2 = 12.29 Factor a perfect square on the left side: (x + -2.7)(x + -2.7) = 12.29 Calculate the square root of the right side: 3.505709629 Break this problem into two subproblems by setting (x + -2.7) equal to 3.505709629 and -3.505709629.Subproblem 1
x + -2.7 = 3.505709629 Simplifying x + -2.7 = 3.505709629 Reorder the terms: -2.7 + x = 3.505709629 Solving -2.7 + x = 3.505709629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = 3.505709629 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = 3.505709629 + 2.7 x = 3.505709629 + 2.7 Combine like terms: 3.505709629 + 2.7 = 6.205709629 x = 6.205709629 Simplifying x = 6.205709629Subproblem 2
x + -2.7 = -3.505709629 Simplifying x + -2.7 = -3.505709629 Reorder the terms: -2.7 + x = -3.505709629 Solving -2.7 + x = -3.505709629 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.7' to each side of the equation. -2.7 + 2.7 + x = -3.505709629 + 2.7 Combine like terms: -2.7 + 2.7 = 0.0 0.0 + x = -3.505709629 + 2.7 x = -3.505709629 + 2.7 Combine like terms: -3.505709629 + 2.7 = -0.805709629 x = -0.805709629 Simplifying x = -0.805709629Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.205709629, -0.805709629}
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