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Simplifying (3x2 + -5x + -72) + (6x2 + 9x) = 0 Reorder the terms: (-72 + -5x + 3x2) + (6x2 + 9x) = 0 Remove parenthesis around (-72 + -5x + 3x2) -72 + -5x + 3x2 + (6x2 + 9x) = 0 Reorder the terms: -72 + -5x + 3x2 + (9x + 6x2) = 0 Remove parenthesis around (9x + 6x2) -72 + -5x + 3x2 + 9x + 6x2 = 0 Reorder the terms: -72 + -5x + 9x + 3x2 + 6x2 = 0 Combine like terms: -5x + 9x = 4x -72 + 4x + 3x2 + 6x2 = 0 Combine like terms: 3x2 + 6x2 = 9x2 -72 + 4x + 9x2 = 0 Solving -72 + 4x + 9x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 9 the coefficient of the squared term: Divide each side by '9'. -8 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '8' to each side of the equation. -8 + 0.4444444444x + 8 + x2 = 0 + 8 Reorder the terms: -8 + 8 + 0.4444444444x + x2 = 0 + 8 Combine like terms: -8 + 8 = 0 0 + 0.4444444444x + x2 = 0 + 8 0.4444444444x + x2 = 0 + 8 Combine like terms: 0 + 8 = 8 0.4444444444x + x2 = 8 The x term is 0.4444444444x. Take half its coefficient (0.2222222222). Square it (0.04938271604) and add it to both sides. Add '0.04938271604' to each side of the equation. 0.4444444444x + 0.04938271604 + x2 = 8 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 8 + 0.04938271604 Combine like terms: 8 + 0.04938271604 = 8.04938271604 0.04938271604 + 0.4444444444x + x2 = 8.04938271604 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 8.04938271604 Calculate the square root of the right side: 2.837143408 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 2.837143408 and -2.837143408.Subproblem 1
x + 0.2222222222 = 2.837143408 Simplifying x + 0.2222222222 = 2.837143408 Reorder the terms: 0.2222222222 + x = 2.837143408 Solving 0.2222222222 + x = 2.837143408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = 2.837143408 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 2.837143408 + -0.2222222222 x = 2.837143408 + -0.2222222222 Combine like terms: 2.837143408 + -0.2222222222 = 2.6149211858 x = 2.6149211858 Simplifying x = 2.6149211858Subproblem 2
x + 0.2222222222 = -2.837143408 Simplifying x + 0.2222222222 = -2.837143408 Reorder the terms: 0.2222222222 + x = -2.837143408 Solving 0.2222222222 + x = -2.837143408 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.2222222222' to each side of the equation. 0.2222222222 + -0.2222222222 + x = -2.837143408 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -2.837143408 + -0.2222222222 x = -2.837143408 + -0.2222222222 Combine like terms: -2.837143408 + -0.2222222222 = -3.0593656302 x = -3.0593656302 Simplifying x = -3.0593656302Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.6149211858, -3.0593656302}
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