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Simplifying 0 = x2 + -5x + -6.67 Reorder the terms: 0 = -6.67 + -5x + x2 Solving 0 = -6.67 + -5x + x2 Solving for variable 'x'. Combine like terms: 0 + 6.67 = 6.67 6.67 + 5x + -1x2 = -6.67 + -5x + x2 + 6.67 + 5x + -1x2 Reorder the terms: 6.67 + 5x + -1x2 = -6.67 + 6.67 + -5x + 5x + x2 + -1x2 Combine like terms: -6.67 + 6.67 = 0.00 6.67 + 5x + -1x2 = 0.00 + -5x + 5x + x2 + -1x2 6.67 + 5x + -1x2 = -5x + 5x + x2 + -1x2 Combine like terms: -5x + 5x = 0 6.67 + 5x + -1x2 = 0 + x2 + -1x2 6.67 + 5x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 6.67 + 5x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. -6.67 + -5x + x2 = 0 Move the constant term to the right: Add '6.67' to each side of the equation. -6.67 + -5x + 6.67 + x2 = 0 + 6.67 Reorder the terms: -6.67 + 6.67 + -5x + x2 = 0 + 6.67 Combine like terms: -6.67 + 6.67 = 0.00 0.00 + -5x + x2 = 0 + 6.67 -5x + x2 = 0 + 6.67 Combine like terms: 0 + 6.67 = 6.67 -5x + x2 = 6.67 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 = 6.67 + 6.25 Reorder the terms: 6.25 + -5x + x2 = 6.67 + 6.25 Combine like terms: 6.67 + 6.25 = 12.92 6.25 + -5x + x2 = 12.92 Factor a perfect square on the left side: (x + -2.5)(x + -2.5) = 12.92 Calculate the square root of the right side: 3.594440151 Break this problem into two subproblems by setting (x + -2.5) equal to 3.594440151 and -3.594440151.Subproblem 1
x + -2.5 = 3.594440151 Simplifying x + -2.5 = 3.594440151 Reorder the terms: -2.5 + x = 3.594440151 Solving -2.5 + x = 3.594440151 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 = 3.594440151 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = 3.594440151 + 2.5 x = 3.594440151 + 2.5 Combine like terms: 3.594440151 + 2.5 = 6.094440151 x = 6.094440151 Simplifying x = 6.094440151Subproblem 2
x + -2.5 = -3.594440151 Simplifying x + -2.5 = -3.594440151 Reorder the terms: -2.5 + x = -3.594440151 Solving -2.5 + x = -3.594440151 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 = -3.594440151 + 2.5 Combine like terms: -2.5 + 2.5 = 0.0 0.0 + x = -3.594440151 + 2.5 x = -3.594440151 + 2.5 Combine like terms: -3.594440151 + 2.5 = -1.094440151 x = -1.094440151 Simplifying x = -1.094440151Solution
The solution to the problem is based on the solutions from the subproblems. x = {6.094440151, -1.094440151}
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