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Simplifying x2 + 7x + 5x + -31 + -30 = 0 Reorder the terms: -31 + -30 + 7x + 5x + x2 = 0 Combine like terms: -31 + -30 = -61 -61 + 7x + 5x + x2 = 0 Combine like terms: 7x + 5x = 12x -61 + 12x + x2 = 0 Solving -61 + 12x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '61' to each side of the equation. -61 + 12x + 61 + x2 = 0 + 61 Reorder the terms: -61 + 61 + 12x + x2 = 0 + 61 Combine like terms: -61 + 61 = 0 0 + 12x + x2 = 0 + 61 12x + x2 = 0 + 61 Combine like terms: 0 + 61 = 61 12x + x2 = 61 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 = 61 + 36 Reorder the terms: 36 + 12x + x2 = 61 + 36 Combine like terms: 61 + 36 = 97 36 + 12x + x2 = 97 Factor a perfect square on the left side: (x + 6)(x + 6) = 97 Calculate the square root of the right side: 9.848857802 Break this problem into two subproblems by setting (x + 6) equal to 9.848857802 and -9.848857802.Subproblem 1
x + 6 = 9.848857802 Simplifying x + 6 = 9.848857802 Reorder the terms: 6 + x = 9.848857802 Solving 6 + x = 9.848857802 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 = 9.848857802 + -6 Combine like terms: 6 + -6 = 0 0 + x = 9.848857802 + -6 x = 9.848857802 + -6 Combine like terms: 9.848857802 + -6 = 3.848857802 x = 3.848857802 Simplifying x = 3.848857802Subproblem 2
x + 6 = -9.848857802 Simplifying x + 6 = -9.848857802 Reorder the terms: 6 + x = -9.848857802 Solving 6 + x = -9.848857802 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 = -9.848857802 + -6 Combine like terms: 6 + -6 = 0 0 + x = -9.848857802 + -6 x = -9.848857802 + -6 Combine like terms: -9.848857802 + -6 = -15.848857802 x = -15.848857802 Simplifying x = -15.848857802Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.848857802, -15.848857802}
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