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Simplifying (2x + 5)(x + -5) = 6 Reorder the terms: (5 + 2x)(x + -5) = 6 Reorder the terms: (5 + 2x)(-5 + x) = 6 Multiply (5 + 2x) * (-5 + x) (5(-5 + x) + 2x * (-5 + x)) = 6 ((-5 * 5 + x * 5) + 2x * (-5 + x)) = 6 ((-25 + 5x) + 2x * (-5 + x)) = 6 (-25 + 5x + (-5 * 2x + x * 2x)) = 6 (-25 + 5x + (-10x + 2x2)) = 6 Combine like terms: 5x + -10x = -5x (-25 + -5x + 2x2) = 6 Solving -25 + -5x + 2x2 = 6 Solving for variable 'x'. Reorder the terms: -25 + -6 + -5x + 2x2 = 6 + -6 Combine like terms: -25 + -6 = -31 -31 + -5x + 2x2 = 6 + -6 Combine like terms: 6 + -6 = 0 -31 + -5x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -15.5 + -2.5x + x2 = 0 Move the constant term to the right: Add '15.5' to each side of the equation. -15.5 + -2.5x + 15.5 + x2 = 0 + 15.5 Reorder the terms: -15.5 + 15.5 + -2.5x + x2 = 0 + 15.5 Combine like terms: -15.5 + 15.5 = 0.0 0.0 + -2.5x + x2 = 0 + 15.5 -2.5x + x2 = 0 + 15.5 Combine like terms: 0 + 15.5 = 15.5 -2.5x + x2 = 15.5 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 15.5 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 15.5 + 1.5625 Combine like terms: 15.5 + 1.5625 = 17.0625 1.5625 + -2.5x + x2 = 17.0625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 17.0625 Calculate the square root of the right side: 4.13067791 Break this problem into two subproblems by setting (x + -1.25) equal to 4.13067791 and -4.13067791.Subproblem 1
x + -1.25 = 4.13067791 Simplifying x + -1.25 = 4.13067791 Reorder the terms: -1.25 + x = 4.13067791 Solving -1.25 + x = 4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 4.13067791 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 4.13067791 + 1.25 x = 4.13067791 + 1.25 Combine like terms: 4.13067791 + 1.25 = 5.38067791 x = 5.38067791 Simplifying x = 5.38067791Subproblem 2
x + -1.25 = -4.13067791 Simplifying x + -1.25 = -4.13067791 Reorder the terms: -1.25 + x = -4.13067791 Solving -1.25 + x = -4.13067791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -4.13067791 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -4.13067791 + 1.25 x = -4.13067791 + 1.25 Combine like terms: -4.13067791 + 1.25 = -2.88067791 x = -2.88067791 Simplifying x = -2.88067791Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.38067791, -2.88067791}
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