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Simplifying 4x(x + -5) = 3x + 7 Reorder the terms: 4x(-5 + x) = 3x + 7 (-5 * 4x + x * 4x) = 3x + 7 (-20x + 4x2) = 3x + 7 Reorder the terms: -20x + 4x2 = 7 + 3x Solving -20x + 4x2 = 7 + 3x Solving for variable 'x'. Reorder the terms: -7 + -20x + -3x + 4x2 = 7 + 3x + -7 + -3x Combine like terms: -20x + -3x = -23x -7 + -23x + 4x2 = 7 + 3x + -7 + -3x Reorder the terms: -7 + -23x + 4x2 = 7 + -7 + 3x + -3x Combine like terms: 7 + -7 = 0 -7 + -23x + 4x2 = 0 + 3x + -3x -7 + -23x + 4x2 = 3x + -3x Combine like terms: 3x + -3x = 0 -7 + -23x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -1.75 + -5.75x + x2 = 0 Move the constant term to the right: Add '1.75' to each side of the equation. -1.75 + -5.75x + 1.75 + x2 = 0 + 1.75 Reorder the terms: -1.75 + 1.75 + -5.75x + x2 = 0 + 1.75 Combine like terms: -1.75 + 1.75 = 0.00 0.00 + -5.75x + x2 = 0 + 1.75 -5.75x + x2 = 0 + 1.75 Combine like terms: 0 + 1.75 = 1.75 -5.75x + x2 = 1.75 The x term is -5.75x. Take half its coefficient (-2.875). Square it (8.265625) and add it to both sides. Add '8.265625' to each side of the equation. -5.75x + 8.265625 + x2 = 1.75 + 8.265625 Reorder the terms: 8.265625 + -5.75x + x2 = 1.75 + 8.265625 Combine like terms: 1.75 + 8.265625 = 10.015625 8.265625 + -5.75x + x2 = 10.015625 Factor a perfect square on the left side: (x + -2.875)(x + -2.875) = 10.015625 Calculate the square root of the right side: 3.164747225 Break this problem into two subproblems by setting (x + -2.875) equal to 3.164747225 and -3.164747225.Subproblem 1
x + -2.875 = 3.164747225 Simplifying x + -2.875 = 3.164747225 Reorder the terms: -2.875 + x = 3.164747225 Solving -2.875 + x = 3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = 3.164747225 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = 3.164747225 + 2.875 x = 3.164747225 + 2.875 Combine like terms: 3.164747225 + 2.875 = 6.039747225 x = 6.039747225 Simplifying x = 6.039747225Subproblem 2
x + -2.875 = -3.164747225 Simplifying x + -2.875 = -3.164747225 Reorder the terms: -2.875 + x = -3.164747225 Solving -2.875 + x = -3.164747225 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.875' to each side of the equation. -2.875 + 2.875 + x = -3.164747225 + 2.875 Combine like terms: -2.875 + 2.875 = 0.000 0.000 + x = -3.164747225 + 2.875 x = -3.164747225 + 2.875 Combine like terms: -3.164747225 + 2.875 = -0.289747225 x = -0.289747225 Simplifying x = -0.289747225Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.039747225, -0.289747225}
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