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Simplifying x2 + 84x + -441 = 0 Reorder the terms: -441 + 84x + x2 = 0 Solving -441 + 84x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '441' to each side of the equation. -441 + 84x + 441 + x2 = 0 + 441 Reorder the terms: -441 + 441 + 84x + x2 = 0 + 441 Combine like terms: -441 + 441 = 0 0 + 84x + x2 = 0 + 441 84x + x2 = 0 + 441 Combine like terms: 0 + 441 = 441 84x + x2 = 441 The x term is 84x. Take half its coefficient (42). Square it (1764) and add it to both sides. Add '1764' to each side of the equation. 84x + 1764 + x2 = 441 + 1764 Reorder the terms: 1764 + 84x + x2 = 441 + 1764 Combine like terms: 441 + 1764 = 2205 1764 + 84x + x2 = 2205 Factor a perfect square on the left side: (x + 42)(x + 42) = 2205 Calculate the square root of the right side: 46.957427527 Break this problem into two subproblems by setting (x + 42) equal to 46.957427527 and -46.957427527.Subproblem 1
x + 42 = 46.957427527 Simplifying x + 42 = 46.957427527 Reorder the terms: 42 + x = 46.957427527 Solving 42 + x = 46.957427527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = 46.957427527 + -42 Combine like terms: 42 + -42 = 0 0 + x = 46.957427527 + -42 x = 46.957427527 + -42 Combine like terms: 46.957427527 + -42 = 4.957427527 x = 4.957427527 Simplifying x = 4.957427527Subproblem 2
x + 42 = -46.957427527 Simplifying x + 42 = -46.957427527 Reorder the terms: 42 + x = -46.957427527 Solving 42 + x = -46.957427527 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-42' to each side of the equation. 42 + -42 + x = -46.957427527 + -42 Combine like terms: 42 + -42 = 0 0 + x = -46.957427527 + -42 x = -46.957427527 + -42 Combine like terms: -46.957427527 + -42 = -88.957427527 x = -88.957427527 Simplifying x = -88.957427527Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.957427527, -88.957427527}
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