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Simplifying x + x2 = 77 Solving x + x2 = 77 Solving for variable 'x'. Reorder the terms: -77 + x + x2 = 77 + -77 Combine like terms: 77 + -77 = 0 -77 + x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '77' to each side of the equation. -77 + x + 77 + x2 = 0 + 77 Reorder the terms: -77 + 77 + x + x2 = 0 + 77 Combine like terms: -77 + 77 = 0 0 + x + x2 = 0 + 77 x + x2 = 0 + 77 Combine like terms: 0 + 77 = 77 x + x2 = 77 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 = 77 + 0.25 Reorder the terms: 0.25 + x + x2 = 77 + 0.25 Combine like terms: 77 + 0.25 = 77.25 0.25 + x + x2 = 77.25 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 77.25 Calculate the square root of the right side: 8.789197916 Break this problem into two subproblems by setting (x + 0.5) equal to 8.789197916 and -8.789197916.Subproblem 1
x + 0.5 = 8.789197916 Simplifying x + 0.5 = 8.789197916 Reorder the terms: 0.5 + x = 8.789197916 Solving 0.5 + x = 8.789197916 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 = 8.789197916 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 8.789197916 + -0.5 x = 8.789197916 + -0.5 Combine like terms: 8.789197916 + -0.5 = 8.289197916 x = 8.289197916 Simplifying x = 8.289197916Subproblem 2
x + 0.5 = -8.789197916 Simplifying x + 0.5 = -8.789197916 Reorder the terms: 0.5 + x = -8.789197916 Solving 0.5 + x = -8.789197916 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 = -8.789197916 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -8.789197916 + -0.5 x = -8.789197916 + -0.5 Combine like terms: -8.789197916 + -0.5 = -9.289197916 x = -9.289197916 Simplifying x = -9.289197916Solution
The solution to the problem is based on the solutions from the subproblems. x = {8.289197916, -9.289197916}
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