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Simplifying 0 = 2x2 + 2x + -77 Reorder the terms: 0 = -77 + 2x + 2x2 Solving 0 = -77 + 2x + 2x2 Solving for variable 'x'. Combine like terms: 0 + 77 = 77 77 + -2x + -2x2 = -77 + 2x + 2x2 + 77 + -2x + -2x2 Reorder the terms: 77 + -2x + -2x2 = -77 + 77 + 2x + -2x + 2x2 + -2x2 Combine like terms: -77 + 77 = 0 77 + -2x + -2x2 = 0 + 2x + -2x + 2x2 + -2x2 77 + -2x + -2x2 = 2x + -2x + 2x2 + -2x2 Combine like terms: 2x + -2x = 0 77 + -2x + -2x2 = 0 + 2x2 + -2x2 77 + -2x + -2x2 = 2x2 + -2x2 Combine like terms: 2x2 + -2x2 = 0 77 + -2x + -2x2 = 0 Begin completing the square. Divide all terms by -2 the coefficient of the squared term: Divide each side by '-2'. -38.5 + x + x2 = 0 Move the constant term to the right: Add '38.5' to each side of the equation. -38.5 + x + 38.5 + x2 = 0 + 38.5 Reorder the terms: -38.5 + 38.5 + x + x2 = 0 + 38.5 Combine like terms: -38.5 + 38.5 = 0.0 0.0 + x + x2 = 0 + 38.5 x + x2 = 0 + 38.5 Combine like terms: 0 + 38.5 = 38.5 x + x2 = 38.5 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. + 0.25 + x2 = 38.5 + 0.25 Combine like terms: + 0.25 = 1.25 1.25 + x2 = 38.5 + 0.25 Combine like terms: 38.5 + 0.25 = 38.75 1.25 + x2 = 38.75 Factor a perfect square on the left side: (x + 0.5)(x + 0.5) = 38.75 Calculate the square root of the right side: 6.224949799 Break this problem into two subproblems by setting (x + 0.5) equal to 6.224949799 and -6.224949799.Subproblem 1
x + 0.5 = 6.224949799 Simplifying x + 0.5 = 6.224949799 Reorder the terms: 0.5 + x = 6.224949799 Solving 0.5 + x = 6.224949799 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 = 6.224949799 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = 6.224949799 + -0.5 x = 6.224949799 + -0.5 Combine like terms: 6.224949799 + -0.5 = 5.724949799 x = 5.724949799 Simplifying x = 5.724949799Subproblem 2
x + 0.5 = -6.224949799 Simplifying x + 0.5 = -6.224949799 Reorder the terms: 0.5 + x = -6.224949799 Solving 0.5 + x = -6.224949799 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 = -6.224949799 + -0.5 Combine like terms: 0.5 + -0.5 = 0.0 0.0 + x = -6.224949799 + -0.5 x = -6.224949799 + -0.5 Combine like terms: -6.224949799 + -0.5 = -6.724949799 x = -6.724949799 Simplifying x = -6.724949799Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.724949799, -6.724949799}
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