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Simplifying (X2) + 4X + -35 = 0 X2 + 4X + -35 = 0 Reorder the terms: -35 + 4X + X2 = 0 Solving -35 + 4X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '35' to each side of the equation. -35 + 4X + 35 + X2 = 0 + 35 Reorder the terms: -35 + 35 + 4X + X2 = 0 + 35 Combine like terms: -35 + 35 = 0 0 + 4X + X2 = 0 + 35 4X + X2 = 0 + 35 Combine like terms: 0 + 35 = 35 4X + X2 = 35 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 = 35 + 4 Reorder the terms: 4 + 4X + X2 = 35 + 4 Combine like terms: 35 + 4 = 39 4 + 4X + X2 = 39 Factor a perfect square on the left side: (X + 2)(X + 2) = 39 Calculate the square root of the right side: 6.244997998 Break this problem into two subproblems by setting (X + 2) equal to 6.244997998 and -6.244997998.Subproblem 1
X + 2 = 6.244997998 Simplifying X + 2 = 6.244997998 Reorder the terms: 2 + X = 6.244997998 Solving 2 + X = 6.244997998 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 = 6.244997998 + -2 Combine like terms: 2 + -2 = 0 0 + X = 6.244997998 + -2 X = 6.244997998 + -2 Combine like terms: 6.244997998 + -2 = 4.244997998 X = 4.244997998 Simplifying X = 4.244997998Subproblem 2
X + 2 = -6.244997998 Simplifying X + 2 = -6.244997998 Reorder the terms: 2 + X = -6.244997998 Solving 2 + X = -6.244997998 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 = -6.244997998 + -2 Combine like terms: 2 + -2 = 0 0 + X = -6.244997998 + -2 X = -6.244997998 + -2 Combine like terms: -6.244997998 + -2 = -8.244997998 X = -8.244997998 Simplifying X = -8.244997998Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.244997998, -8.244997998}
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