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Simplifying x2 + 26x + -224 = 0 Reorder the terms: -224 + 26x + x2 = 0 Solving -224 + 26x + 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 + 26x + 224 + x2 = 0 + 224 Reorder the terms: -224 + 224 + 26x + x2 = 0 + 224 Combine like terms: -224 + 224 = 0 0 + 26x + x2 = 0 + 224 26x + x2 = 0 + 224 Combine like terms: 0 + 224 = 224 26x + x2 = 224 The x term is 26x. Take half its coefficient (13). Square it (169) and add it to both sides. Add '169' to each side of the equation. 26x + 169 + x2 = 224 + 169 Reorder the terms: 169 + 26x + x2 = 224 + 169 Combine like terms: 224 + 169 = 393 169 + 26x + x2 = 393 Factor a perfect square on the left side: (x + 13)(x + 13) = 393 Calculate the square root of the right side: 19.824227602 Break this problem into two subproblems by setting (x + 13) equal to 19.824227602 and -19.824227602.Subproblem 1
x + 13 = 19.824227602 Simplifying x + 13 = 19.824227602 Reorder the terms: 13 + x = 19.824227602 Solving 13 + x = 19.824227602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = 19.824227602 + -13 Combine like terms: 13 + -13 = 0 0 + x = 19.824227602 + -13 x = 19.824227602 + -13 Combine like terms: 19.824227602 + -13 = 6.824227602 x = 6.824227602 Simplifying x = 6.824227602Subproblem 2
x + 13 = -19.824227602 Simplifying x + 13 = -19.824227602 Reorder the terms: 13 + x = -19.824227602 Solving 13 + x = -19.824227602 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-13' to each side of the equation. 13 + -13 + x = -19.824227602 + -13 Combine like terms: 13 + -13 = 0 0 + x = -19.824227602 + -13 x = -19.824227602 + -13 Combine like terms: -19.824227602 + -13 = -32.824227602 x = -32.824227602 Simplifying x = -32.824227602Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.824227602, -32.824227602}
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