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Simplifying x2 + x + -8436 = 0 Reorder the terms: -8436 + x + x2 = 0 Solving -8436 + x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '8436' to each side of the equation. -8436 + x + 8436 + x2 = 0 + 8436 Reorder the terms: -8436 + 8436 + x + x2 = 0 + 8436 Combine like terms: -8436 + 8436 = 0 0 + x + x2 = 0 + 8436 x + x2 = 0 + 8436 Combine like terms: 0 + 8436 = 8436 x + x2 = 8436 The x term is x. Take half its coefficient (0.5). Square it (0.25) and add it to both sides. Add '0.25' to each side of the equation. x + 0.25 + x2 = 8436 + 0.25 Reorder the terms: 0.25 + x + x2 = 8436 + 0.25 Combine like terms: 8436 + 0.25 = 8436.25 0.25 + x + x2 = 8436.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 8436.25 Calculate the square root of the right side: 91.849060964 Break this problem into two subproblems by setting (x + 0.5) equal to 91.849060964 and -91.849060964.Subproblem 1
x + 0.5 = 91.849060964 Simplifying x + 0.5 = 91.849060964 Reorder the terms: 0.5 + x = 91.849060964 Solving 0.5 + x = 91.849060964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = 91.849060964 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 91.849060964 + -0.5 x = 91.849060964 + -0.5 Combine like terms: 91.849060964 + -0.5 = 91.349060964 x = 91.349060964 Simplifying x = 91.349060964Subproblem 2
x + 0.5 = -91.849060964 Simplifying x + 0.5 = -91.849060964 Reorder the terms: 0.5 + x = -91.849060964 Solving 0.5 + x = -91.849060964 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.5' to each side of the equation. 0.5 + -0.5 + x = -91.849060964 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -91.849060964 + -0.5 x = -91.849060964 + -0.5 Combine like terms: -91.849060964 + -0.5 = -92.349060964 x = -92.349060964 Simplifying x = -92.349060964Solution
The solution to the problem is based on the solutions from the subproblems. x = {91.349060964, -92.349060964}
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