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Simplifying x(x + 4) = 209 Reorder the terms: x(4 + x) = 209 (4 * x + x * x) = 209 (4x + x2) = 209 Solving 4x + x2 = 209 Solving for variable 'x'. Reorder the terms: -209 + 4x + x2 = 209 + -209 Combine like terms: 209 + -209 = 0 -209 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '209' to each side of the equation. -209 + 4x + 209 + x2 = 0 + 209 Reorder the terms: -209 + 209 + 4x + x2 = 0 + 209 Combine like terms: -209 + 209 = 0 0 + 4x + x2 = 0 + 209 4x + x2 = 0 + 209 Combine like terms: 0 + 209 = 209 4x + x2 = 209 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 = 209 + 4 Reorder the terms: 4 + 4x + x2 = 209 + 4 Combine like terms: 209 + 4 = 213 4 + 4x + x2 = 213 Factor a perfect square on the left side: (x + 2)(x + 2) = 213 Calculate the square root of the right side: 14.594519519 Break this problem into two subproblems by setting (x + 2) equal to 14.594519519 and -14.594519519.Subproblem 1
x + 2 = 14.594519519 Simplifying x + 2 = 14.594519519 Reorder the terms: 2 + x = 14.594519519 Solving 2 + x = 14.594519519 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 = 14.594519519 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14.594519519 + -2 x = 14.594519519 + -2 Combine like terms: 14.594519519 + -2 = 12.594519519 x = 12.594519519 Simplifying x = 12.594519519Subproblem 2
x + 2 = -14.594519519 Simplifying x + 2 = -14.594519519 Reorder the terms: 2 + x = -14.594519519 Solving 2 + x = -14.594519519 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 = -14.594519519 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14.594519519 + -2 x = -14.594519519 + -2 Combine like terms: -14.594519519 + -2 = -16.594519519 x = -16.594519519 Simplifying x = -16.594519519Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.594519519, -16.594519519}
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