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Simplifying X2 + 8X + -49 = 0 Reorder the terms: -49 + 8X + X2 = 0 Solving -49 + 8X + X2 = 0 Solving for variable 'X'. Begin completing the square. Move the constant term to the right: Add '49' to each side of the equation. -49 + 8X + 49 + X2 = 0 + 49 Reorder the terms: -49 + 49 + 8X + X2 = 0 + 49 Combine like terms: -49 + 49 = 0 0 + 8X + X2 = 0 + 49 8X + X2 = 0 + 49 Combine like terms: 0 + 49 = 49 8X + X2 = 49 The X term is 8X. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8X + 16 + X2 = 49 + 16 Reorder the terms: 16 + 8X + X2 = 49 + 16 Combine like terms: 49 + 16 = 65 16 + 8X + X2 = 65 Factor a perfect square on the left side: (X + 4)(X + 4) = 65 Calculate the square root of the right side: 8.062257748 Break this problem into two subproblems by setting (X + 4) equal to 8.062257748 and -8.062257748.Subproblem 1
X + 4 = 8.062257748 Simplifying X + 4 = 8.062257748 Reorder the terms: 4 + X = 8.062257748 Solving 4 + X = 8.062257748 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + X = 8.062257748 + -4 Combine like terms: 4 + -4 = 0 0 + X = 8.062257748 + -4 X = 8.062257748 + -4 Combine like terms: 8.062257748 + -4 = 4.062257748 X = 4.062257748 Simplifying X = 4.062257748Subproblem 2
X + 4 = -8.062257748 Simplifying X + 4 = -8.062257748 Reorder the terms: 4 + X = -8.062257748 Solving 4 + X = -8.062257748 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + X = -8.062257748 + -4 Combine like terms: 4 + -4 = 0 0 + X = -8.062257748 + -4 X = -8.062257748 + -4 Combine like terms: -8.062257748 + -4 = -12.062257748 X = -12.062257748 Simplifying X = -12.062257748Solution
The solution to the problem is based on the solutions from the subproblems. X = {4.062257748, -12.062257748}
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