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Simplifying (2x + 3)(x + -5) = 10 Reorder the terms: (3 + 2x)(x + -5) = 10 Reorder the terms: (3 + 2x)(-5 + x) = 10 Multiply (3 + 2x) * (-5 + x) (3(-5 + x) + 2x * (-5 + x)) = 10 ((-5 * 3 + x * 3) + 2x * (-5 + x)) = 10 ((-15 + 3x) + 2x * (-5 + x)) = 10 (-15 + 3x + (-5 * 2x + x * 2x)) = 10 (-15 + 3x + (-10x + 2x2)) = 10 Combine like terms: 3x + -10x = -7x (-15 + -7x + 2x2) = 10 Solving -15 + -7x + 2x2 = 10 Solving for variable 'x'. Reorder the terms: -15 + -10 + -7x + 2x2 = 10 + -10 Combine like terms: -15 + -10 = -25 -25 + -7x + 2x2 = 10 + -10 Combine like terms: 10 + -10 = 0 -25 + -7x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -12.5 + -3.5x + x2 = 0 Move the constant term to the right: Add '12.5' to each side of the equation. -12.5 + -3.5x + 12.5 + x2 = 0 + 12.5 Reorder the terms: -12.5 + 12.5 + -3.5x + x2 = 0 + 12.5 Combine like terms: -12.5 + 12.5 = 0.0 0.0 + -3.5x + x2 = 0 + 12.5 -3.5x + x2 = 0 + 12.5 Combine like terms: 0 + 12.5 = 12.5 -3.5x + x2 = 12.5 The x term is -3.5x. Take half its coefficient (-1.75). Square it (3.0625) and add it to both sides. Add '3.0625' to each side of the equation. -3.5x + 3.0625 + x2 = 12.5 + 3.0625 Reorder the terms: 3.0625 + -3.5x + x2 = 12.5 + 3.0625 Combine like terms: 12.5 + 3.0625 = 15.5625 3.0625 + -3.5x + x2 = 15.5625 Factor a perfect square on the left side: (x + -1.75)(x + -1.75) = 15.5625 Calculate the square root of the right side: 3.94493346 Break this problem into two subproblems by setting (x + -1.75) equal to 3.94493346 and -3.94493346.Subproblem 1
x + -1.75 = 3.94493346 Simplifying x + -1.75 = 3.94493346 Reorder the terms: -1.75 + x = 3.94493346 Solving -1.75 + x = 3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = 3.94493346 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = 3.94493346 + 1.75 x = 3.94493346 + 1.75 Combine like terms: 3.94493346 + 1.75 = 5.69493346 x = 5.69493346 Simplifying x = 5.69493346Subproblem 2
x + -1.75 = -3.94493346 Simplifying x + -1.75 = -3.94493346 Reorder the terms: -1.75 + x = -3.94493346 Solving -1.75 + x = -3.94493346 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.75' to each side of the equation. -1.75 + 1.75 + x = -3.94493346 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + x = -3.94493346 + 1.75 x = -3.94493346 + 1.75 Combine like terms: -3.94493346 + 1.75 = -2.19493346 x = -2.19493346 Simplifying x = -2.19493346Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.69493346, -2.19493346}
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