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Simplifying x2 + -22x + 39 = 7x + 3 Reorder the terms: 39 + -22x + x2 = 7x + 3 Reorder the terms: 39 + -22x + x2 = 3 + 7x Solving 39 + -22x + x2 = 3 + 7x Solving for variable 'x'. Reorder the terms: 39 + -3 + -22x + -7x + x2 = 3 + 7x + -3 + -7x Combine like terms: 39 + -3 = 36 36 + -22x + -7x + x2 = 3 + 7x + -3 + -7x Combine like terms: -22x + -7x = -29x 36 + -29x + x2 = 3 + 7x + -3 + -7x Reorder the terms: 36 + -29x + x2 = 3 + -3 + 7x + -7x Combine like terms: 3 + -3 = 0 36 + -29x + x2 = 0 + 7x + -7x 36 + -29x + x2 = 7x + -7x Combine like terms: 7x + -7x = 0 36 + -29x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '-36' to each side of the equation. 36 + -29x + -36 + x2 = 0 + -36 Reorder the terms: 36 + -36 + -29x + x2 = 0 + -36 Combine like terms: 36 + -36 = 0 0 + -29x + x2 = 0 + -36 -29x + x2 = 0 + -36 Combine like terms: 0 + -36 = -36 -29x + x2 = -36 The x term is -29x. Take half its coefficient (-14.5). Square it (210.25) and add it to both sides. Add '210.25' to each side of the equation. -29x + 210.25 + x2 = -36 + 210.25 Reorder the terms: 210.25 + -29x + x2 = -36 + 210.25 Combine like terms: -36 + 210.25 = 174.25 210.25 + -29x + x2 = 174.25 Factor a perfect square on the left side: (x + -14.5)(x + -14.5) = 174.25 Calculate the square root of the right side: 13.200378782 Break this problem into two subproblems by setting (x + -14.5) equal to 13.200378782 and -13.200378782.Subproblem 1
x + -14.5 = 13.200378782 Simplifying x + -14.5 = 13.200378782 Reorder the terms: -14.5 + x = 13.200378782 Solving -14.5 + x = 13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = 13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = 13.200378782 + 14.5 x = 13.200378782 + 14.5 Combine like terms: 13.200378782 + 14.5 = 27.700378782 x = 27.700378782 Simplifying x = 27.700378782Subproblem 2
x + -14.5 = -13.200378782 Simplifying x + -14.5 = -13.200378782 Reorder the terms: -14.5 + x = -13.200378782 Solving -14.5 + x = -13.200378782 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '14.5' to each side of the equation. -14.5 + 14.5 + x = -13.200378782 + 14.5 Combine like terms: -14.5 + 14.5 = 0.0 0.0 + x = -13.200378782 + 14.5 x = -13.200378782 + 14.5 Combine like terms: -13.200378782 + 14.5 = 1.299621218 x = 1.299621218 Simplifying x = 1.299621218Solution
The solution to the problem is based on the solutions from the subproblems. x = {27.700378782, 1.299621218}
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