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Simplifying (8x2 + -2x + 16) + (2x2 + 8x + -73) = 0 Reorder the terms: (16 + -2x + 8x2) + (2x2 + 8x + -73) = 0 Remove parenthesis around (16 + -2x + 8x2) 16 + -2x + 8x2 + (2x2 + 8x + -73) = 0 Reorder the terms: 16 + -2x + 8x2 + (-73 + 8x + 2x2) = 0 Remove parenthesis around (-73 + 8x + 2x2) 16 + -2x + 8x2 + -73 + 8x + 2x2 = 0 Reorder the terms: 16 + -73 + -2x + 8x + 8x2 + 2x2 = 0 Combine like terms: 16 + -73 = -57 -57 + -2x + 8x + 8x2 + 2x2 = 0 Combine like terms: -2x + 8x = 6x -57 + 6x + 8x2 + 2x2 = 0 Combine like terms: 8x2 + 2x2 = 10x2 -57 + 6x + 10x2 = 0 Solving -57 + 6x + 10x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 10 the coefficient of the squared term: Divide each side by '10'. -5.7 + 0.6x + x2 = 0.0 Move the constant term to the right: Add '5.7' to each side of the equation. -5.7 + 0.6x + 5.7 + x2 = 0.0 + 5.7 Reorder the terms: -5.7 + 5.7 + 0.6x + x2 = 0.0 + 5.7 Combine like terms: -5.7 + 5.7 = 0.0 0.0 + 0.6x + x2 = 0.0 + 5.7 0.6x + x2 = 0.0 + 5.7 Combine like terms: 0.0 + 5.7 = 5.7 0.6x + x2 = 5.7 The x term is 0.6x. Take half its coefficient (0.3). Square it (0.09) and add it to both sides. Add '0.09' to each side of the equation. 0.6x + 0.09 + x2 = 5.7 + 0.09 Reorder the terms: 0.09 + 0.6x + x2 = 5.7 + 0.09 Combine like terms: 5.7 + 0.09 = 5.79 0.09 + 0.6x + x2 = 5.79 Factor a perfect square on the left side: (x + 0.3)(x + 0.3) = 5.79 Calculate the square root of the right side: 2.406241883 Break this problem into two subproblems by setting (x + 0.3) equal to 2.406241883 and -2.406241883.Subproblem 1
x + 0.3 = 2.406241883 Simplifying x + 0.3 = 2.406241883 Reorder the terms: 0.3 + x = 2.406241883 Solving 0.3 + x = 2.406241883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = 2.406241883 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = 2.406241883 + -0.3 x = 2.406241883 + -0.3 Combine like terms: 2.406241883 + -0.3 = 2.106241883 x = 2.106241883 Simplifying x = 2.106241883Subproblem 2
x + 0.3 = -2.406241883 Simplifying x + 0.3 = -2.406241883 Reorder the terms: 0.3 + x = -2.406241883 Solving 0.3 + x = -2.406241883 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.3' to each side of the equation. 0.3 + -0.3 + x = -2.406241883 + -0.3 Combine like terms: 0.3 + -0.3 = 0.0 0.0 + x = -2.406241883 + -0.3 x = -2.406241883 + -0.3 Combine like terms: -2.406241883 + -0.3 = -2.706241883 x = -2.706241883 Simplifying x = -2.706241883Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.106241883, -2.706241883}
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