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Simplifying x2 + 4x = 286 Reorder the terms: 4x + x2 = 286 Solving 4x + x2 = 286 Solving for variable 'x'. Reorder the terms: -286 + 4x + x2 = 286 + -286 Combine like terms: 286 + -286 = 0 -286 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '286' to each side of the equation. -286 + 4x + 286 + x2 = 0 + 286 Reorder the terms: -286 + 286 + 4x + x2 = 0 + 286 Combine like terms: -286 + 286 = 0 0 + 4x + x2 = 0 + 286 4x + x2 = 0 + 286 Combine like terms: 0 + 286 = 286 4x + x2 = 286 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 = 286 + 4 Reorder the terms: 4 + 4x + x2 = 286 + 4 Combine like terms: 286 + 4 = 290 4 + 4x + x2 = 290 Factor a perfect square on the left side: (x + 2)(x + 2) = 290 Calculate the square root of the right side: 17.029386366 Break this problem into two subproblems by setting (x + 2) equal to 17.029386366 and -17.029386366.Subproblem 1
x + 2 = 17.029386366 Simplifying x + 2 = 17.029386366 Reorder the terms: 2 + x = 17.029386366 Solving 2 + x = 17.029386366 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 = 17.029386366 + -2 Combine like terms: 2 + -2 = 0 0 + x = 17.029386366 + -2 x = 17.029386366 + -2 Combine like terms: 17.029386366 + -2 = 15.029386366 x = 15.029386366 Simplifying x = 15.029386366Subproblem 2
x + 2 = -17.029386366 Simplifying x + 2 = -17.029386366 Reorder the terms: 2 + x = -17.029386366 Solving 2 + x = -17.029386366 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 = -17.029386366 + -2 Combine like terms: 2 + -2 = 0 0 + x = -17.029386366 + -2 x = -17.029386366 + -2 Combine like terms: -17.029386366 + -2 = -19.029386366 x = -19.029386366 Simplifying x = -19.029386366Solution
The solution to the problem is based on the solutions from the subproblems. x = {15.029386366, -19.029386366}
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