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Simplifying 0 = x2 + 5x + -256 Reorder the terms: 0 = -256 + 5x + x2 Solving 0 = -256 + 5x + x2 Solving for variable 'x'. Combine like terms: 0 + 256 = 256 256 + -5x + -1x2 = -256 + 5x + x2 + 256 + -5x + -1x2 Reorder the terms: 256 + -5x + -1x2 = -256 + 256 + 5x + -5x + x2 + -1x2 Combine like terms: -256 + 256 = 0 256 + -5x + -1x2 = 0 + 5x + -5x + x2 + -1x2 256 + -5x + -1x2 = 5x + -5x + x2 + -1x2 Combine like terms: 5x + -5x = 0 256 + -5x + -1x2 = 0 + x2 + -1x2 256 + -5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 256 + -5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -256 + 5x + x2 = 0 Move the constant term to the right: Add '256' to each side of the equation. -256 + 5x + 256 + x2 = 0 + 256 Reorder the terms: -256 + 256 + 5x + x2 = 0 + 256 Combine like terms: -256 + 256 = 0 0 + 5x + x2 = 0 + 256 5x + x2 = 0 + 256 Combine like terms: 0 + 256 = 256 5x + x2 = 256 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = 256 + 6.25 Reorder the terms: 6.25 + 5x + x2 = 256 + 6.25 Combine like terms: 256 + 6.25 = 262.25 6.25 + 5x + x2 = 262.25 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 262.25 Calculate the square root of the right side: 16.194134741 Break this problem into two subproblems by setting (x + 2.5) equal to 16.194134741 and -16.194134741.Subproblem 1
x + 2.5 = 16.194134741 Simplifying x + 2.5 = 16.194134741 Reorder the terms: 2.5 + x = 16.194134741 Solving 2.5 + x = 16.194134741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 16.194134741 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 16.194134741 + -2.5 x = 16.194134741 + -2.5 Combine like terms: 16.194134741 + -2.5 = 13.694134741 x = 13.694134741 Simplifying x = 13.694134741Subproblem 2
x + 2.5 = -16.194134741 Simplifying x + 2.5 = -16.194134741 Reorder the terms: 2.5 + x = -16.194134741 Solving 2.5 + x = -16.194134741 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -16.194134741 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -16.194134741 + -2.5 x = -16.194134741 + -2.5 Combine like terms: -16.194134741 + -2.5 = -18.694134741 x = -18.694134741 Simplifying x = -18.694134741Solution
The solution to the problem is based on the solutions from the subproblems. x = {13.694134741, -18.694134741}
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