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Simplifying x2 + 4x + -225 = 0 Reorder the terms: -225 + 4x + x2 = 0 Solving -225 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '225' to each side of the equation. -225 + 4x + 225 + x2 = 0 + 225 Reorder the terms: -225 + 225 + 4x + x2 = 0 + 225 Combine like terms: -225 + 225 = 0 0 + 4x + x2 = 0 + 225 4x + x2 = 0 + 225 Combine like terms: 0 + 225 = 225 4x + x2 = 225 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 = 225 + 4 Reorder the terms: 4 + 4x + x2 = 225 + 4 Combine like terms: 225 + 4 = 229 4 + 4x + x2 = 229 Factor a perfect square on the left side: (x + 2)(x + 2) = 229 Calculate the square root of the right side: 15.13274595 Break this problem into two subproblems by setting (x + 2) equal to 15.13274595 and -15.13274595.Subproblem 1
x + 2 = 15.13274595 Simplifying x + 2 = 15.13274595 Reorder the terms: 2 + x = 15.13274595 Solving 2 + x = 15.13274595 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 = 15.13274595 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.13274595 + -2 x = 15.13274595 + -2 Combine like terms: 15.13274595 + -2 = 13.13274595 x = 13.13274595 Simplifying x = 13.13274595Subproblem 2
x + 2 = -15.13274595 Simplifying x + 2 = -15.13274595 Reorder the terms: 2 + x = -15.13274595 Solving 2 + x = -15.13274595 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 = -15.13274595 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.13274595 + -2 x = -15.13274595 + -2 Combine like terms: -15.13274595 + -2 = -17.13274595 x = -17.13274595 Simplifying x = -17.13274595Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.13274595, -17.13274595}
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