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Simplifying (X + -6)(X + -34) = 1 Reorder the terms: (-6 + X)(X + -34) = 1 Reorder the terms: (-6 + X)(-34 + X) = 1 Multiply (-6 + X) * (-34 + X) (-6(-34 + X) + X(-34 + X)) = 1 ((-34 * -6 + X * -6) + X(-34 + X)) = 1 ((204 + -6X) + X(-34 + X)) = 1 (204 + -6X + (-34 * X + X * X)) = 1 (204 + -6X + (-34X + X2)) = 1 Combine like terms: -6X + -34X = -40X (204 + -40X + X2) = 1 Solving 204 + -40X + X2 = 1 Solving for variable 'X'. Reorder the terms: 204 + -1 + -40X + X2 = 1 + -1 Combine like terms: 204 + -1 = 203 203 + -40X + X2 = 1 + -1 Combine like terms: 1 + -1 = 0 203 + -40X + X2 = 0 Begin completing the square. Move the constant term to the right: Add '-203' to each side of the equation. 203 + -40X + -203 + X2 = 0 + -203 Reorder the terms: 203 + -203 + -40X + X2 = 0 + -203 Combine like terms: 203 + -203 = 0 0 + -40X + X2 = 0 + -203 -40X + X2 = 0 + -203 Combine like terms: 0 + -203 = -203 -40X + X2 = -203 The X term is -40X. Take half its coefficient (-20). Square it (400) and add it to both sides. Add '400' to each side of the equation. -40X + 400 + X2 = -203 + 400 Reorder the terms: 400 + -40X + X2 = -203 + 400 Combine like terms: -203 + 400 = 197 400 + -40X + X2 = 197 Factor a perfect square on the left side: (X + -20)(X + -20) = 197 Calculate the square root of the right side: 14.035668848 Break this problem into two subproblems by setting (X + -20) equal to 14.035668848 and -14.035668848.Subproblem 1
X + -20 = 14.035668848 Simplifying X + -20 = 14.035668848 Reorder the terms: -20 + X = 14.035668848 Solving -20 + X = 14.035668848 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + X = 14.035668848 + 20 Combine like terms: -20 + 20 = 0 0 + X = 14.035668848 + 20 X = 14.035668848 + 20 Combine like terms: 14.035668848 + 20 = 34.035668848 X = 34.035668848 Simplifying X = 34.035668848Subproblem 2
X + -20 = -14.035668848 Simplifying X + -20 = -14.035668848 Reorder the terms: -20 + X = -14.035668848 Solving -20 + X = -14.035668848 Solving for variable 'X'. Move all terms containing X to the left, all other terms to the right. Add '20' to each side of the equation. -20 + 20 + X = -14.035668848 + 20 Combine like terms: -20 + 20 = 0 0 + X = -14.035668848 + 20 X = -14.035668848 + 20 Combine like terms: -14.035668848 + 20 = 5.964331152 X = 5.964331152 Simplifying X = 5.964331152Solution
The solution to the problem is based on the solutions from the subproblems. X = {34.035668848, 5.964331152}
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