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Simplifying (x2 + 3x + 6) + (7x + -4) = 0 Reorder the terms: (6 + 3x + x2) + (7x + -4) = 0 Remove parenthesis around (6 + 3x + x2) 6 + 3x + x2 + (7x + -4) = 0 Reorder the terms: 6 + 3x + x2 + (-4 + 7x) = 0 Remove parenthesis around (-4 + 7x) 6 + 3x + x2 + -4 + 7x = 0 Reorder the terms: 6 + -4 + 3x + 7x + x2 = 0 Combine like terms: 6 + -4 = 2 2 + 3x + 7x + x2 = 0 Combine like terms: 3x + 7x = 10x 2 + 10x + x2 = 0 Solving 2 + 10x + x2 = 0 Solving for variable 'x'. Begin completing the square. Move the constant term to the right: Add '-2' to each side of the equation. 2 + 10x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 10x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 10x + x2 = 0 + -2 10x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 10x + x2 = -2 The x term is 10x. Take half its coefficient (5). Square it (25) and add it to both sides. Add '25' to each side of the equation. 10x + 25 + x2 = -2 + 25 Reorder the terms: 25 + 10x + x2 = -2 + 25 Combine like terms: -2 + 25 = 23 25 + 10x + x2 = 23 Factor a perfect square on the left side: (x + 5)(x + 5) = 23 Calculate the square root of the right side: 4.795831523 Break this problem into two subproblems by setting (x + 5) equal to 4.795831523 and -4.795831523.Subproblem 1
x + 5 = 4.795831523 Simplifying x + 5 = 4.795831523 Reorder the terms: 5 + x = 4.795831523 Solving 5 + x = 4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = 4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + x = 4.795831523 + -5 x = 4.795831523 + -5 Combine like terms: 4.795831523 + -5 = -0.204168477 x = -0.204168477 Simplifying x = -0.204168477Subproblem 2
x + 5 = -4.795831523 Simplifying x + 5 = -4.795831523 Reorder the terms: 5 + x = -4.795831523 Solving 5 + x = -4.795831523 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + x = -4.795831523 + -5 Combine like terms: 5 + -5 = 0 0 + x = -4.795831523 + -5 x = -4.795831523 + -5 Combine like terms: -4.795831523 + -5 = -9.795831523 x = -9.795831523 Simplifying x = -9.795831523Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.204168477, -9.795831523}
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