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Simplifying x2 + 7x = 9 + -5x Reorder the terms: 7x + x2 = 9 + -5x Solving 7x + x2 = 9 + -5x Solving for variable 'x'. Reorder the terms: -9 + 7x + 5x + x2 = 9 + -5x + -9 + 5x Combine like terms: 7x + 5x = 12x -9 + 12x + x2 = 9 + -5x + -9 + 5x Reorder the terms: -9 + 12x + x2 = 9 + -9 + -5x + 5x Combine like terms: 9 + -9 = 0 -9 + 12x + x2 = 0 + -5x + 5x -9 + 12x + x2 = -5x + 5x Combine like terms: -5x + 5x = 0 -9 + 12x + x2 = 0 Begin completing the square. Move the constant term to the right: Add '9' to each side of the equation. -9 + 12x + 9 + x2 = 0 + 9 Reorder the terms: -9 + 9 + 12x + x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 12x + x2 = 0 + 9 12x + x2 = 0 + 9 Combine like terms: 0 + 9 = 9 12x + x2 = 9 The x term is 12x. Take half its coefficient (6). Square it (36) and add it to both sides. Add '36' to each side of the equation. 12x + 36 + x2 = 9 + 36 Reorder the terms: 36 + 12x + x2 = 9 + 36 Combine like terms: 9 + 36 = 45 36 + 12x + x2 = 45 Factor a perfect square on the left side: (x + 6)(x + 6) = 45 Calculate the square root of the right side: 6.708203933 Break this problem into two subproblems by setting (x + 6) equal to 6.708203933 and -6.708203933.Subproblem 1
x + 6 = 6.708203933 Simplifying x + 6 = 6.708203933 Reorder the terms: 6 + x = 6.708203933 Solving 6 + x = 6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = 6.708203933 + -6 Combine like terms: 6 + -6 = 0 0 + x = 6.708203933 + -6 x = 6.708203933 + -6 Combine like terms: 6.708203933 + -6 = 0.708203933 x = 0.708203933 Simplifying x = 0.708203933Subproblem 2
x + 6 = -6.708203933 Simplifying x + 6 = -6.708203933 Reorder the terms: 6 + x = -6.708203933 Solving 6 + x = -6.708203933 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + x = -6.708203933 + -6 Combine like terms: 6 + -6 = 0 0 + x = -6.708203933 + -6 x = -6.708203933 + -6 Combine like terms: -6.708203933 + -6 = -12.708203933 x = -12.708203933 Simplifying x = -12.708203933Solution
The solution to the problem is based on the solutions from the subproblems. x = {0.708203933, -12.708203933}
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