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Simplifying x2 + 4x + -224 = 0 Reorder the terms: -224 + 4x + x2 = 0 Solving -224 + 4x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '224' to each side of the equation. -224 + 4x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 4x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 4x + x2 = 0 + 224 4x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 4x + x2 = 224 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 = 224 + 4 Reorder the terms: 4 + 4x + x2 = 224 + 4 Combine like terms: 224 + 4 = 228 4 + 4x + x2 = 228 Factor a perfect square on the left side: (x + 2)(x + 2) = 228 Calculate the square root of the right side: 15.099668871 Break this problem into two subproblems by setting (x + 2) equal to 15.099668871 and -15.099668871.Subproblem 1
x + 2 = 15.099668871 Simplifying x + 2 = 15.099668871 Reorder the terms: 2 + x = 15.099668871 Solving 2 + x = 15.099668871 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 = 15.099668871 + -2 Combine like terms: 2 + -2 = 0 0 + x = 15.099668871 + -2 x = 15.099668871 + -2 Combine like terms: 15.099668871 + -2 = 13.099668871 x = 13.099668871 Simplifying x = 13.099668871Subproblem 2
x + 2 = -15.099668871 Simplifying x + 2 = -15.099668871 Reorder the terms: 2 + x = -15.099668871 Solving 2 + x = -15.099668871 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 = -15.099668871 + -2 Combine like terms: 2 + -2 = 0 0 + x = -15.099668871 + -2 x = -15.099668871 + -2 Combine like terms: -15.099668871 + -2 = -17.099668871 x = -17.099668871 Simplifying x = -17.099668871Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.099668871, -17.099668871}
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