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Simplifying 4x(x + -5) + 2 = x + 3 Reorder the terms: 4x(-5 + x) + 2 = x + 3 (-5 * 4x + x * 4x) + 2 = x + 3 (-20x + 4x2) + 2 = x + 3 Reorder the terms: 2 + -20x + 4x2 = x + 3 Reorder the terms: 2 + -20x + 4x2 = 3 + x Solving 2 + -20x + 4x2 = 3 + x Solving for variable 'x'. Reorder the terms: 2 + -3 + -20x + -1x + 4x2 = 3 + x + -3 + -1x Combine like terms: 2 + -3 = -1 -1 + -20x + -1x + 4x2 = 3 + x + -3 + -1x Combine like terms: -20x + -1x = -21x -1 + -21x + 4x2 = 3 + x + -3 + -1x Reorder the terms: -1 + -21x + 4x2 = 3 + -3 + x + -1x Combine like terms: 3 + -3 = 0 -1 + -21x + 4x2 = 0 + x + -1x -1 + -21x + 4x2 = x + -1x Combine like terms: x + -1x = 0 -1 + -21x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -0.25 + -5.25x + x2 = 0 Move the constant term to the right: Add '0.25' to each side of the equation. -0.25 + -5.25x + 0.25 + x2 = 0 + 0.25 Reorder the terms: -0.25 + 0.25 + -5.25x + x2 = 0 + 0.25 Combine like terms: -0.25 + 0.25 = 0.00 0.00 + -5.25x + x2 = 0 + 0.25 -5.25x + x2 = 0 + 0.25 Combine like terms: 0 + 0.25 = 0.25 -5.25x + x2 = 0.25 The x term is -5.25x. Take half its coefficient (-2.625). Square it (6.890625) and add it to both sides. Add '6.890625' to each side of the equation. -5.25x + 6.890625 + x2 = 0.25 + 6.890625 Reorder the terms: 6.890625 + -5.25x + x2 = 0.25 + 6.890625 Combine like terms: 0.25 + 6.890625 = 7.140625 6.890625 + -5.25x + x2 = 7.140625 Factor a perfect square on the left side: (x + -2.625)(x + -2.625) = 7.140625 Calculate the square root of the right side: 2.672194791 Break this problem into two subproblems by setting (x + -2.625) equal to 2.672194791 and -2.672194791.Subproblem 1
x + -2.625 = 2.672194791 Simplifying x + -2.625 = 2.672194791 Reorder the terms: -2.625 + x = 2.672194791 Solving -2.625 + x = 2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = 2.672194791 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = 2.672194791 + 2.625 x = 2.672194791 + 2.625 Combine like terms: 2.672194791 + 2.625 = 5.297194791 x = 5.297194791 Simplifying x = 5.297194791Subproblem 2
x + -2.625 = -2.672194791 Simplifying x + -2.625 = -2.672194791 Reorder the terms: -2.625 + x = -2.672194791 Solving -2.625 + x = -2.672194791 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '2.625' to each side of the equation. -2.625 + 2.625 + x = -2.672194791 + 2.625 Combine like terms: -2.625 + 2.625 = 0.000 0.000 + x = -2.672194791 + 2.625 x = -2.672194791 + 2.625 Combine like terms: -2.672194791 + 2.625 = -0.047194791 x = -0.047194791 Simplifying x = -0.047194791Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.297194791, -0.047194791}
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