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Simplifying 2x2 + 16x + -57 = 0 Reorder the terms: -57 + 16x + 2x2 = 0 Solving -57 + 16x + 2x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. -28.5 + 8x + x2 = 0 Move the constant term to the right: Add '28.5' to each side of the equation. -28.5 + 8x + 28.5 + x2 = 0 + 28.5 Reorder the terms: -28.5 + 28.5 + 8x + x2 = 0 + 28.5 Combine like terms: -28.5 + 28.5 = 0.0 0.0 + 8x + x2 = 0 + 28.5 8x + x2 = 0 + 28.5 Combine like terms: 0 + 28.5 = 28.5 8x + x2 = 28.5 The x term is 8x. Take half its coefficient (4). Square it (16) and add it to both sides. Add '16' to each side of the equation. 8x + 16 + x2 = 28.5 + 16 Reorder the terms: 16 + 8x + x2 = 28.5 + 16 Combine like terms: 28.5 + 16 = 44.5 16 + 8x + x2 = 44.5 Factor a perfect square on the left side: (x + 4)(x + 4) = 44.5 Calculate the square root of the right side: 6.670832032 Break this problem into two subproblems by setting (x + 4) equal to 6.670832032 and -6.670832032.Subproblem 1
x + 4 = 6.670832032 Simplifying x + 4 = 6.670832032 Reorder the terms: 4 + x = 6.670832032 Solving 4 + x = 6.670832032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = 6.670832032 + -4 Combine like terms: 4 + -4 = 0 0 + x = 6.670832032 + -4 x = 6.670832032 + -4 Combine like terms: 6.670832032 + -4 = 2.670832032 x = 2.670832032 Simplifying x = 2.670832032Subproblem 2
x + 4 = -6.670832032 Simplifying x + 4 = -6.670832032 Reorder the terms: 4 + x = -6.670832032 Solving 4 + x = -6.670832032 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + x = -6.670832032 + -4 Combine like terms: 4 + -4 = 0 0 + x = -6.670832032 + -4 x = -6.670832032 + -4 Combine like terms: -6.670832032 + -4 = -10.670832032 x = -10.670832032 Simplifying x = -10.670832032Solution
The solution to the problem is based on the solutions from the subproblems. x = {2.670832032, -10.670832032}
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