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Simplifying x2 + 4x + 9 = 213 Reorder the terms: 9 + 4x + x2 = 213 Solving 9 + 4x + x2 = 213 Solving for variable 'x'. Reorder the terms: 9 + -213 + 4x + x2 = 213 + -213 Combine like terms: 9 + -213 = -204 -204 + 4x + x2 = 213 + -213 Combine like terms: 213 + -213 = 0 -204 + 4x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '204' to each side of the equation. -204 + 4x + 204 + x2 = 0 + 204 Reorder the terms: -204 + 204 + 4x + x2 = 0 + 204 Combine like terms: -204 + 204 = 0 0 + 4x + x2 = 0 + 204 4x + x2 = 0 + 204 Combine like terms: 0 + 204 = 204 4x + x2 = 204 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 = 204 + 4 Reorder the terms: 4 + 4x + x2 = 204 + 4 Combine like terms: 204 + 4 = 208 4 + 4x + x2 = 208 Factor a perfect square on the left side: (x + 2)(x + 2) = 208 Calculate the square root of the right side: 14.422205102 Break this problem into two subproblems by setting (x + 2) equal to 14.422205102 and -14.422205102.Subproblem 1
x + 2 = 14.422205102 Simplifying x + 2 = 14.422205102 Reorder the terms: 2 + x = 14.422205102 Solving 2 + x = 14.422205102 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 = 14.422205102 + -2 Combine like terms: 2 + -2 = 0 0 + x = 14.422205102 + -2 x = 14.422205102 + -2 Combine like terms: 14.422205102 + -2 = 12.422205102 x = 12.422205102 Simplifying x = 12.422205102Subproblem 2
x + 2 = -14.422205102 Simplifying x + 2 = -14.422205102 Reorder the terms: 2 + x = -14.422205102 Solving 2 + x = -14.422205102 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 = -14.422205102 + -2 Combine like terms: 2 + -2 = 0 0 + x = -14.422205102 + -2 x = -14.422205102 + -2 Combine like terms: -14.422205102 + -2 = -16.422205102 x = -16.422205102 Simplifying x = -16.422205102Solution
The solution to the problem is based on the solutions from the subproblems. x = {12.422205102, -16.422205102}
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