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Simplifying 5x2 + 40x + 16 = 0 Reorder the terms: 16 + 40x + 5x2 = 0 Solving 16 + 40x + 5x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 5 the coefficient of the squared term: Divide each side by '5'. 3.2 + 8x + x2 = 0 Move the constant term to the right: Add '-3.2' to each side of the equation. 3.2 + 8x + -3.2 + x2 = 0 + -3.2 Reorder the terms: 3.2 + -3.2 + 8x + x2 = 0 + -3.2 Combine like terms: 3.2 + -3.2 = 0.0 0.0 + 8x + x2 = 0 + -3.2 8x + x2 = 0 + -3.2 Combine like terms: 0 + -3.2 = -3.2 8x + x2 = -3.2 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 = -3.2 + 16 Reorder the terms: 16 + 8x + x2 = -3.2 + 16 Combine like terms: -3.2 + 16 = 12.8 16 + 8x + x2 = 12.8 Factor a perfect square on the left side: (x + 4)(x + 4) = 12.8 Calculate the square root of the right side: 3.577708764 Break this problem into two subproblems by setting (x + 4) equal to 3.577708764 and -3.577708764.Subproblem 1
x + 4 = 3.577708764 Simplifying x + 4 = 3.577708764 Reorder the terms: 4 + x = 3.577708764 Solving 4 + x = 3.577708764 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 = 3.577708764 + -4 Combine like terms: 4 + -4 = 0 0 + x = 3.577708764 + -4 x = 3.577708764 + -4 Combine like terms: 3.577708764 + -4 = -0.422291236 x = -0.422291236 Simplifying x = -0.422291236Subproblem 2
x + 4 = -3.577708764 Simplifying x + 4 = -3.577708764 Reorder the terms: 4 + x = -3.577708764 Solving 4 + x = -3.577708764 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 = -3.577708764 + -4 Combine like terms: 4 + -4 = 0 0 + x = -3.577708764 + -4 x = -3.577708764 + -4 Combine like terms: -3.577708764 + -4 = -7.577708764 x = -7.577708764 Simplifying x = -7.577708764Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.422291236, -7.577708764}
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