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Simplifying (x + -5)(4x + 5) = 2 Reorder the terms: (-5 + x)(4x + 5) = 2 Reorder the terms: (-5 + x)(5 + 4x) = 2 Multiply (-5 + x) * (5 + 4x) (-5(5 + 4x) + x(5 + 4x)) = 2 ((5 * -5 + 4x * -5) + x(5 + 4x)) = 2 ((-25 + -20x) + x(5 + 4x)) = 2 (-25 + -20x + (5 * x + 4x * x)) = 2 (-25 + -20x + (5x + 4x2)) = 2 Combine like terms: -20x + 5x = -15x (-25 + -15x + 4x2) = 2 Solving -25 + -15x + 4x2 = 2 Solving for variable 'x'. Reorder the terms: -25 + -2 + -15x + 4x2 = 2 + -2 Combine like terms: -25 + -2 = -27 -27 + -15x + 4x2 = 2 + -2 Combine like terms: 2 + -2 = 0 -27 + -15x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -6.75 + -3.75x + x2 = 0 Move the constant term to the right: Add '6.75' to each side of the equation. -6.75 + -3.75x + 6.75 + x2 = 0 + 6.75 Reorder the terms: -6.75 + 6.75 + -3.75x + x2 = 0 + 6.75 Combine like terms: -6.75 + 6.75 = 0.00 0.00 + -3.75x + x2 = 0 + 6.75 -3.75x + x2 = 0 + 6.75 Combine like terms: 0 + 6.75 = 6.75 -3.75x + x2 = 6.75 The x term is -3.75x. Take half its coefficient (-1.875). Square it (3.515625) and add it to both sides. Add '3.515625' to each side of the equation. -3.75x + 3.515625 + x2 = 6.75 + 3.515625 Reorder the terms: 3.515625 + -3.75x + x2 = 6.75 + 3.515625 Combine like terms: 6.75 + 3.515625 = 10.265625 3.515625 + -3.75x + x2 = 10.265625 Factor a perfect square on the left side: (x + -1.875)(x + -1.875) = 10.265625 Calculate the square root of the right side: 3.204001404 Break this problem into two subproblems by setting (x + -1.875) equal to 3.204001404 and -3.204001404.Subproblem 1
x + -1.875 = 3.204001404 Simplifying x + -1.875 = 3.204001404 Reorder the terms: -1.875 + x = 3.204001404 Solving -1.875 + x = 3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = 3.204001404 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = 3.204001404 + 1.875 x = 3.204001404 + 1.875 Combine like terms: 3.204001404 + 1.875 = 5.079001404 x = 5.079001404 Simplifying x = 5.079001404Subproblem 2
x + -1.875 = -3.204001404 Simplifying x + -1.875 = -3.204001404 Reorder the terms: -1.875 + x = -3.204001404 Solving -1.875 + x = -3.204001404 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.875' to each side of the equation. -1.875 + 1.875 + x = -3.204001404 + 1.875 Combine like terms: -1.875 + 1.875 = 0.000 0.000 + x = -3.204001404 + 1.875 x = -3.204001404 + 1.875 Combine like terms: -3.204001404 + 1.875 = -1.329001404 x = -1.329001404 Simplifying x = -1.329001404Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.079001404, -1.329001404}
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