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Simplifying (5x2 + -4x + -52) + (4x2 + 8x) = 0 Reorder the terms: (-52 + -4x + 5x2) + (4x2 + 8x) = 0 Remove parenthesis around (-52 + -4x + 5x2) -52 + -4x + 5x2 + (4x2 + 8x) = 0 Reorder the terms: -52 + -4x + 5x2 + (8x + 4x2) = 0 Remove parenthesis around (8x + 4x2) -52 + -4x + 5x2 + 8x + 4x2 = 0 Reorder the terms: -52 + -4x + 8x + 5x2 + 4x2 = 0 Combine like terms: -4x + 8x = 4x -52 + 4x + 5x2 + 4x2 = 0 Combine like terms: 5x2 + 4x2 = 9x2 -52 + 4x + 9x2 = 0 Solving -52 + 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'. -5.777777778 + 0.4444444444x + x2 = 0 Move the constant term to the right: Add '5.777777778' to each side of the equation. -5.777777778 + 0.4444444444x + 5.777777778 + x2 = 0 + 5.777777778 Reorder the terms: -5.777777778 + 5.777777778 + 0.4444444444x + x2 = 0 + 5.777777778 Combine like terms: -5.777777778 + 5.777777778 = 0.000000000 0.000000000 + 0.4444444444x + x2 = 0 + 5.777777778 0.4444444444x + x2 = 0 + 5.777777778 Combine like terms: 0 + 5.777777778 = 5.777777778 0.4444444444x + x2 = 5.777777778 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 = 5.777777778 + 0.04938271604 Reorder the terms: 0.04938271604 + 0.4444444444x + x2 = 5.777777778 + 0.04938271604 Combine like terms: 5.777777778 + 0.04938271604 = 5.82716049404 0.04938271604 + 0.4444444444x + x2 = 5.82716049404 Factor a perfect square on the left side: (x + 0.2222222222)(x + 0.2222222222) = 5.82716049404 Calculate the square root of the right side: 2.41395122 Break this problem into two subproblems by setting (x + 0.2222222222) equal to 2.41395122 and -2.41395122.Subproblem 1
x + 0.2222222222 = 2.41395122 Simplifying x + 0.2222222222 = 2.41395122 Reorder the terms: 0.2222222222 + x = 2.41395122 Solving 0.2222222222 + x = 2.41395122 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 = 2.41395122 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = 2.41395122 + -0.2222222222 x = 2.41395122 + -0.2222222222 Combine like terms: 2.41395122 + -0.2222222222 = 2.1917289978 x = 2.1917289978 Simplifying x = 2.1917289978Subproblem 2
x + 0.2222222222 = -2.41395122 Simplifying x + 0.2222222222 = -2.41395122 Reorder the terms: 0.2222222222 + x = -2.41395122 Solving 0.2222222222 + x = -2.41395122 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 = -2.41395122 + -0.2222222222 Combine like terms: 0.2222222222 + -0.2222222222 = 0.0000000000 0.0000000000 + x = -2.41395122 + -0.2222222222 x = -2.41395122 + -0.2222222222 Combine like terms: -2.41395122 + -0.2222222222 = -2.6361734422 x = -2.6361734422 Simplifying x = -2.6361734422Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.1917289978, -2.6361734422}
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