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Simplifying 4x(x + -5) = 5x + 1 Reorder the terms: 4x(-5 + x) = 5x + 1 (-5 * 4x + x * 4x) = 5x + 1 (-20x + 4x2) = 5x + 1 Reorder the terms: -20x + 4x2 = 1 + 5x Solving -20x + 4x2 = 1 + 5x Solving for variable 'x'. Reorder the terms: -1 + -20x + -5x + 4x2 = 1 + 5x + -1 + -5x Combine like terms: -20x + -5x = -25x -1 + -25x + 4x2 = 1 + 5x + -1 + -5x Reorder the terms: -1 + -25x + 4x2 = 1 + -1 + 5x + -5x Combine like terms: 1 + -1 = 0 -1 + -25x + 4x2 = 0 + 5x + -5x -1 + -25x + 4x2 = 5x + -5x Combine like terms: 5x + -5x = 0 -1 + -25x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -6.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -6.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -6.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -6.25x + x2 = 0 + 0.25 -6.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -6.25x + x2 = 0.25 The x term is -6.25x. Take half its coefficient (-3.125). Square it (9.765625) and add it to both sides. Add '9.765625' to each side of the equation. -6.25x + 9.765625 + x2 = 0.25 + 9.765625 Reorder the terms: 9.765625 + -6.25x + x2 = 0.25 + 9.765625 Combine like terms: 0.25 + 9.765625 = 10.015625 9.765625 + -6.25x + x2 = 10.015625 Factor a perfect square on the left side: (x + -3.125)(x + -3.125) = 10.015625 Calculate the square root of the right side: 3.164747225 Break this problem into two subproblems by setting (x + -3.125) equal to 3.164747225 and -3.164747225.Subproblem 1
x + -3.125 = 3.164747225 Simplifying x + -3.125 = 3.164747225 Reorder the terms: -3.125 + x = 3.164747225 Solving -3.125 + x = 3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = 3.164747225 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = 3.164747225 + 3.125 x = 3.164747225 + 3.125 Combine like terms: 3.164747225 + 3.125 = 6.289747225 x = 6.289747225 Simplifying x = 6.289747225Subproblem 2
x + -3.125 = -3.164747225 Simplifying x + -3.125 = -3.164747225 Reorder the terms: -3.125 + x = -3.164747225 Solving -3.125 + x = -3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3.125' to each side of the equation. -3.125 + 3.125 + x = -3.164747225 + 3.125 Combine like terms: -3.125 + 3.125 = 0.000 0.000 + x = -3.164747225 + 3.125 x = -3.164747225 + 3.125 Combine like terms: -3.164747225 + 3.125 = -0.039747225 x = -0.039747225 Simplifying x = -0.039747225Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.289747225, -0.039747225}
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