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Simplifying 4x(x + 5) = 7x + 38 Reorder the terms: 4x(5 + x) = 7x + 38 (5 * 4x + x * 4x) = 7x + 38 (20x + 4x2) = 7x + 38 Reorder the terms: 20x + 4x2 = 38 + 7x Solving 20x + 4x2 = 38 + 7x Solving for variable 'x'. Reorder the terms: -38 + 20x + -7x + 4x2 = 38 + 7x + -38 + -7x Combine like terms: 20x + -7x = 13x -38 + 13x + 4x2 = 38 + 7x + -38 + -7x Reorder the terms: -38 + 13x + 4x2 = 38 + -38 + 7x + -7x Combine like terms: 38 + -38 = 0 -38 + 13x + 4x2 = 0 + 7x + -7x -38 + 13x + 4x2 = 7x + -7x Combine like terms: 7x + -7x = 0 -38 + 13x + 4x2 = 0 Begin completing the square. Divide all terms by 4 the coefficient of the squared term: Divide each side by '4'. -9.5 + 3.25x + x2 = 0 Move the constant term to the right: Add '9.5' to each side of the equation. -9.5 + 3.25x + 9.5 + x2 = 0 + 9.5 Reorder the terms: -9.5 + 9.5 + 3.25x + x2 = 0 + 9.5 Combine like terms: -9.5 + 9.5 = 0.0 0.0 + 3.25x + x2 = 0 + 9.5 3.25x + x2 = 0 + 9.5 Combine like terms: 0 + 9.5 = 9.5 3.25x + x2 = 9.5 The x term is 3.25x. Take half its coefficient (1.625). Square it (2.640625) and add it to both sides. Add '2.640625' to each side of the equation. 3.25x + 2.640625 + x2 = 9.5 + 2.640625 Reorder the terms: 2.640625 + 3.25x + x2 = 9.5 + 2.640625 Combine like terms: 9.5 + 2.640625 = 12.140625 2.640625 + 3.25x + x2 = 12.140625 Factor a perfect square on the left side: (x + 1.625)(x + 1.625) = 12.140625 Calculate the square root of the right side: 3.484339966 Break this problem into two subproblems by setting (x + 1.625) equal to 3.484339966 and -3.484339966.Subproblem 1
x + 1.625 = 3.484339966 Simplifying x + 1.625 = 3.484339966 Reorder the terms: 1.625 + x = 3.484339966 Solving 1.625 + x = 3.484339966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = 3.484339966 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = 3.484339966 + -1.625 x = 3.484339966 + -1.625 Combine like terms: 3.484339966 + -1.625 = 1.859339966 x = 1.859339966 Simplifying x = 1.859339966Subproblem 2
x + 1.625 = -3.484339966 Simplifying x + 1.625 = -3.484339966 Reorder the terms: 1.625 + x = -3.484339966 Solving 1.625 + x = -3.484339966 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-1.625' to each side of the equation. 1.625 + -1.625 + x = -3.484339966 + -1.625 Combine like terms: 1.625 + -1.625 = 0.000 0.000 + x = -3.484339966 + -1.625 x = -3.484339966 + -1.625 Combine like terms: -3.484339966 + -1.625 = -5.109339966 x = -5.109339966 Simplifying x = -5.109339966Solution
The solution to the problem is based on the solutions from the subproblems. x = {1.859339966, -5.109339966}
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