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Simplifying (5x + 3)(x + -5) = 5 Reorder the terms: (3 + 5x)(x + -5) = 5 Reorder the terms: (3 + 5x)(-5 + x) = 5 Multiply (3 + 5x) * (-5 + x) (3(-5 + x) + 5x * (-5 + x)) = 5 ((-5 * 3 + x * 3) + 5x * (-5 + x)) = 5 ((-15 + 3x) + 5x * (-5 + x)) = 5 (-15 + 3x + (-5 * 5x + x * 5x)) = 5 (-15 + 3x + (-25x + 5x2)) = 5 Combine like terms: 3x + -25x = -22x (-15 + -22x + 5x2) = 5 Solving -15 + -22x + 5x2 = 5 Solving for variable 'x'. Reorder the terms: -15 + -5 + -22x + 5x2 = 5 + -5 Combine like terms: -15 + -5 = -20 -20 + -22x + 5x2 = 5 + -5 Combine like terms: 5 + -5 = 0 -20 + -22x + 5x2 = 0 Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. -4 + -4.4x + x2 = 0 Move the constant term to the right: Add '4' to each side of the equation. -4 + -4.4x + 4 + x2 = 0 + 4 Reorder the terms: -4 + 4 + -4.4x + x2 = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -4.4x + x2 = 0 + 4 -4.4x + x2 = 0 + 4 Combine like terms: 0 + 4 = 4 -4.4x + x2 = 4 The x term is -4.4x. Take half its coefficient (-2.2). Square it (4.84) and add it to both sides. Add '4.84' to each side of the equation. -4.4x + 4.84 + x2 = 4 + 4.84 Reorder the terms: 4.84 + -4.4x + x2 = 4 + 4.84 Combine like terms: 4 + 4.84 = 8.84 4.84 + -4.4x + x2 = 8.84 Factor a perfect square on the left side: (x + -2.2)(x + -2.2) = 8.84 Calculate the square root of the right side: 2.973213749 Break this problem into two subproblems by setting (x + -2.2) equal to 2.973213749 and -2.973213749.Subproblem 1
x + -2.2 = 2.973213749 Simplifying x + -2.2 = 2.973213749 Reorder the terms: -2.2 + x = 2.973213749 Solving -2.2 + x = 2.973213749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = 2.973213749 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = 2.973213749 + 2.2 x = 2.973213749 + 2.2 Combine like terms: 2.973213749 + 2.2 = 5.173213749 x = 5.173213749 Simplifying x = 5.173213749Subproblem 2
x + -2.2 = -2.973213749 Simplifying x + -2.2 = -2.973213749 Reorder the terms: -2.2 + x = -2.973213749 Solving -2.2 + x = -2.973213749 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.2' to each side of the equation. -2.2 + 2.2 + x = -2.973213749 + 2.2 Combine like terms: -2.2 + 2.2 = 0.0 0.0 + x = -2.973213749 + 2.2 x = -2.973213749 + 2.2 Combine like terms: -2.973213749 + 2.2 = -0.773213749 x = -0.773213749 Simplifying x = -0.773213749Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.173213749, -0.773213749}
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