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Simplifying 0 = x2 + -3x + -555 Reorder the terms: 0 = -555 + -3x + x2 Solving 0 = -555 + -3x + x2 Solving for variable 'x'. Combine like terms: 0 + 555 = 555 555 + 3x + -1x2 = -555 + -3x + x2 + 555 + 3x + -1x2 Reorder the terms: 555 + 3x + -1x2 = -555 + 555 + -3x + 3x + x2 + -1x2 Combine like terms: -555 + 555 = 0 555 + 3x + -1x2 = 0 + -3x + 3x + x2 + -1x2 555 + 3x + -1x2 = -3x + 3x + x2 + -1x2 Combine like terms: -3x + 3x = 0 555 + 3x + -1x2 = 0 + x2 + -1x2 555 + 3x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 555 + 3x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -555 + -3x + x2 = 0 Move the constant term to the right: Add '555' to each side of the equation. -555 + -3x + 555 + x2 = 0 + 555 Reorder the terms: -555 + 555 + -3x + x2 = 0 + 555 Combine like terms: -555 + 555 = 0 0 + -3x + x2 = 0 + 555 -3x + x2 = 0 + 555 Combine like terms: 0 + 555 = 555 -3x + x2 = 555 The x term is -3x. Take half its coefficient (-1.5). Square it (2.25) and add it to both sides. Add '2.25' to each side of the equation. -3x + 2.25 + x2 = 555 + 2.25 Reorder the terms: 2.25 + -3x + x2 = 555 + 2.25 Combine like terms: 555 + 2.25 = 557.25 2.25 + -3x + x2 = 557.25 Factor a perfect square on the left side: (x + -1.5)(x + -1.5) = 557.25 Calculate the square root of the right side: 23.606143268 Break this problem into two subproblems by setting (x + -1.5) equal to 23.606143268 and -23.606143268.Subproblem 1
x + -1.5 = 23.606143268 Simplifying x + -1.5 = 23.606143268 Reorder the terms: -1.5 + x = 23.606143268 Solving -1.5 + x = 23.606143268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = 23.606143268 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = 23.606143268 + 1.5 x = 23.606143268 + 1.5 Combine like terms: 23.606143268 + 1.5 = 25.106143268 x = 25.106143268 Simplifying x = 25.106143268Subproblem 2
x + -1.5 = -23.606143268 Simplifying x + -1.5 = -23.606143268 Reorder the terms: -1.5 + x = -23.606143268 Solving -1.5 + x = -23.606143268 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.5' to each side of the equation. -1.5 + 1.5 + x = -23.606143268 + 1.5 Combine like terms: -1.5 + 1.5 = 0.0 0.0 + x = -23.606143268 + 1.5 x = -23.606143268 + 1.5 Combine like terms: -23.606143268 + 1.5 = -22.106143268 x = -22.106143268 Simplifying x = -22.106143268Solution
The solution to the problem is based on the solutions from the subproblems. x = {25.106143268, -22.106143268}
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