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Simplifying x(x + 4) = 243 Reorder the terms: x(4 + x) = 243 (4 * x + x * x) = 243 (4x + x2) = 243 Solving 4x + x2 = 243 Solving for variable 'x'. Reorder the terms: -243 + 4x + x2 = 243 + -243 Combine like terms: 243 + -243 = 0 -243 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '243' to each side of the equation. -243 + 4x + 243 + x2 = 0 + 243 Reorder the terms: -243 + 243 + 4x + x2 = 0 + 243 Combine like terms: -243 + 243 = 0 0 + 4x + x2 = 0 + 243 4x + x2 = 0 + 243 Combine like terms: 0 + 243 = 243 4x + x2 = 243 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 = 243 + 4 Reorder the terms: 4 + 4x + x2 = 243 + 4 Combine like terms: 243 + 4 = 247 4 + 4x + x2 = 247 Factor a perfect square on the left side: (x + 2)(x + 2) = 247 Calculate the square root of the right side: 15.716233646 Break this problem into two subproblems by setting (x + 2) equal to 15.716233646 and -15.716233646.Subproblem 1
x + 2 = 15.716233646 Simplifying x + 2 = 15.716233646 Reorder the terms: 2 + x = 15.716233646 Solving 2 + x = 15.716233646 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 = 15.716233646 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.716233646 + -2 x = 15.716233646 + -2 Combine like terms: 15.716233646 + -2 = 13.716233646 x = 13.716233646 Simplifying x = 13.716233646Subproblem 2
x + 2 = -15.716233646 Simplifying x + 2 = -15.716233646 Reorder the terms: 2 + x = -15.716233646 Solving 2 + x = -15.716233646 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 = -15.716233646 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.716233646 + -2 x = -15.716233646 + -2 Combine like terms: -15.716233646 + -2 = -17.716233646 x = -17.716233646 Simplifying x = -17.716233646Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.716233646, -17.716233646}
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