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Simplifying x(x + 4) = 2420 Reorder the terms: x(4 + x) = 2420 (4 * x + x * x) = 2420 (4x + x2) = 2420 Solving 4x + x2 = 2420 Solving for variable 'x'. Reorder the terms: -2420 + 4x + x2 = 2420 + -2420 Combine like terms: 2420 + -2420 = 0 -2420 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '2420' to each side of the equation. -2420 + 4x + 2420 + x2 = 0 + 2420 Reorder the terms: -2420 + 2420 + 4x + x2 = 0 + 2420 Combine like terms: -2420 + 2420 = 0 0 + 4x + x2 = 0 + 2420 4x + x2 = 0 + 2420 Combine like terms: 0 + 2420 = 2420 4x + x2 = 2420 The x term is 4x. Take half its coefficient (2). Square it (4) and add it to both sides. Add '4' to each side of the equation. 4x + 4 + x2 = 2420 + 4 Reorder the terms: 4 + 4x + x2 = 2420 + 4 Combine like terms: 2420 + 4 = 2424 4 + 4x + x2 = 2424 Factor a perfect square on the left side: (x + 2)(x + 2) = 2424 Calculate the square root of the right side: 49.2341345 Break this problem into two subproblems by setting (x + 2) equal to 49.2341345 and -49.2341345.Subproblem 1
x + 2 = 49.2341345 Simplifying x + 2 = 49.2341345 Reorder the terms: 2 + x = 49.2341345 Solving 2 + x = 49.2341345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = 49.2341345 + -2 Combine like terms: 2 + -2 = 0 0 + x = 49.2341345 + -2 x = 49.2341345 + -2 Combine like terms: 49.2341345 + -2 = 47.2341345 x = 47.2341345 Simplifying x = 47.2341345Subproblem 2
x + 2 = -49.2341345 Simplifying x + 2 = -49.2341345 Reorder the terms: 2 + x = -49.2341345 Solving 2 + x = -49.2341345 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + x = -49.2341345 + -2 Combine like terms: 2 + -2 = 0 0 + x = -49.2341345 + -2 x = -49.2341345 + -2 Combine like terms: -49.2341345 + -2 = -51.2341345 x = -51.2341345 Simplifying x = -51.2341345Solution
The solution to the problem is based on the solutions from the subproblems. x = {47.2341345, -51.2341345}
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