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Simplifying x2 + 182x + 84 = 0 Reorder the terms: 84 + 182x + x2 = 0 Solving 84 + 182x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-84' to each side of the equation. 84 + 182x + -84 + x2 = 0 + -84 Reorder the terms: 84 + -84 + 182x + x2 = 0 + -84 Combine like terms: 84 + -84 = 0 0 + 182x + x2 = 0 + -84 182x + x2 = 0 + -84 Combine like terms: 0 + -84 = -84 182x + x2 = -84 The x term is 182x. Take half its coefficient (91). Square it (8281) and add it to both sides. Add '8281' to each side of the equation. 182x + 8281 + x2 = -84 + 8281 Reorder the terms: 8281 + 182x + x2 = -84 + 8281 Combine like terms: -84 + 8281 = 8197 8281 + 182x + x2 = 8197 Factor a perfect square on the left side: (x + 91)(x + 91) = 8197 Calculate the square root of the right side: 90.537285137 Break this problem into two subproblems by setting (x + 91) equal to 90.537285137 and -90.537285137.Subproblem 1
x + 91 = 90.537285137 Simplifying x + 91 = 90.537285137 Reorder the terms: 91 + x = 90.537285137 Solving 91 + x = 90.537285137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-91' to each side of the equation. 91 + -91 + x = 90.537285137 + -91 Combine like terms: 91 + -91 = 0 0 + x = 90.537285137 + -91 x = 90.537285137 + -91 Combine like terms: 90.537285137 + -91 = -0.462714863 x = -0.462714863 Simplifying x = -0.462714863Subproblem 2
x + 91 = -90.537285137 Simplifying x + 91 = -90.537285137 Reorder the terms: 91 + x = -90.537285137 Solving 91 + x = -90.537285137 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-91' to each side of the equation. 91 + -91 + x = -90.537285137 + -91 Combine like terms: 91 + -91 = 0 0 + x = -90.537285137 + -91 x = -90.537285137 + -91 Combine like terms: -90.537285137 + -91 = -181.537285137 x = -181.537285137 Simplifying x = -181.537285137Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.462714863, -181.537285137}
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