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Simplifying 0 = x2 + -6x + 2.25 Reorder the terms: 0 = 2.25 + -6x + x2 Solving 0 = 2.25 + -6x + x2 Solving for variable 'x'. Combine like terms: 0 + -2.25 = -2.25 -2.25 + 6x + -1x2 = 2.25 + -6x + x2 + -2.25 + 6x + -1x2 Reorder the terms: -2.25 + 6x + -1x2 = 2.25 + -2.25 + -6x + 6x + x2 + -1x2 Combine like terms: 2.25 + -2.25 = 0.00 -2.25 + 6x + -1x2 = 0.00 + -6x + 6x + x2 + -1x2 -2.25 + 6x + -1x2 = -6x + 6x + x2 + -1x2 Combine like terms: -6x + 6x = 0 -2.25 + 6x + -1x2 = 0 + x2 + -1x2 -2.25 + 6x + -1x2 = x2 + -1x2 Combine like terms: x2 + -1x2 = 0 -2.25 + 6x + -1x2 = 0 Begin completing the square. Divide all terms by -1 the coefficient of the squared term: Divide each side by '-1'. 2.25 + -6x + x2 = 0 Move the constant term to the right: Add '-2.25' to each side of the equation. 2.25 + -6x + -2.25 + x2 = 0 + -2.25 Reorder the terms: 2.25 + -2.25 + -6x + x2 = 0 + -2.25 Combine like terms: 2.25 + -2.25 = 0.00 0.00 + -6x + x2 = 0 + -2.25 -6x + x2 = 0 + -2.25 Combine like terms: 0 + -2.25 = -2.25 -6x + x2 = -2.25 The x term is -6x. Take half its coefficient (-3). Square it (9) and add it to both sides. Add '9' to each side of the equation. -6x + 9 + x2 = -2.25 + 9 Reorder the terms: 9 + -6x + x2 = -2.25 + 9 Combine like terms: -2.25 + 9 = 6.75 9 + -6x + x2 = 6.75 Factor a perfect square on the left side: (x + -3)(x + -3) = 6.75 Calculate the square root of the right side: 2.598076211 Break this problem into two subproblems by setting (x + -3) equal to 2.598076211 and -2.598076211.Subproblem 1
x + -3 = 2.598076211 Simplifying x + -3 = 2.598076211 Reorder the terms: -3 + x = 2.598076211 Solving -3 + x = 2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = 2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + x = 2.598076211 + 3 x = 2.598076211 + 3 Combine like terms: 2.598076211 + 3 = 5.598076211 x = 5.598076211 Simplifying x = 5.598076211Subproblem 2
x + -3 = -2.598076211 Simplifying x + -3 = -2.598076211 Reorder the terms: -3 + x = -2.598076211 Solving -3 + x = -2.598076211 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + x = -2.598076211 + 3 Combine like terms: -3 + 3 = 0 0 + x = -2.598076211 + 3 x = -2.598076211 + 3 Combine like terms: -2.598076211 + 3 = 0.401923789 x = 0.401923789 Simplifying x = 0.401923789Solution
The solution to the problem is based on the solutions from the subproblems. x = {5.598076211, 0.401923789}
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