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Simplifying 16x2 + 80x + 25 = 0 Reorder the terms: 25 + 80x + 16x2 = 0 Solving 25 + 80x + 16x2 = 0 Solving for variable 'x'. Begin completing the square. Divide all terms by 16 the coefficient of the squared term: Divide each side by '16'. 1.5625 + 5x + x2 = 0 Move the constant term to the right: Add '-1.5625' to each side of the equation. 1.5625 + 5x + -1.5625 + x2 = 0 + -1.5625 Reorder the terms: 1.5625 + -1.5625 + 5x + x2 = 0 + -1.5625 Combine like terms: 1.5625 + -1.5625 = 0.0000 0.0000 + 5x + x2 = 0 + -1.5625 5x + x2 = 0 + -1.5625 Combine like terms: 0 + -1.5625 = -1.5625 5x + x2 = -1.5625 The x term is 5x. Take half its coefficient (2.5). Square it (6.25) and add it to both sides. Add '6.25' to each side of the equation. 5x + 6.25 + x2 = -1.5625 + 6.25 Reorder the terms: 6.25 + 5x + x2 = -1.5625 + 6.25 Combine like terms: -1.5625 + 6.25 = 4.6875 6.25 + 5x + x2 = 4.6875 Factor a perfect square on the left side: (x + 2.5)(x + 2.5) = 4.6875 Calculate the square root of the right side: 2.165063509 Break this problem into two subproblems by setting (x + 2.5) equal to 2.165063509 and -2.165063509.Subproblem 1
x + 2.5 = 2.165063509 Simplifying x + 2.5 = 2.165063509 Reorder the terms: 2.5 + x = 2.165063509 Solving 2.5 + x = 2.165063509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = 2.165063509 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = 2.165063509 + -2.5 x = 2.165063509 + -2.5 Combine like terms: 2.165063509 + -2.5 = -0.334936491 x = -0.334936491 Simplifying x = -0.334936491Subproblem 2
x + 2.5 = -2.165063509 Simplifying x + 2.5 = -2.165063509 Reorder the terms: 2.5 + x = -2.165063509 Solving 2.5 + x = -2.165063509 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-2.5' to each side of the equation. 2.5 + -2.5 + x = -2.165063509 + -2.5 Combine like terms: 2.5 + -2.5 = 0.0 0.0 + x = -2.165063509 + -2.5 x = -2.165063509 + -2.5 Combine like terms: -2.165063509 + -2.5 = -4.665063509 x = -4.665063509 Simplifying x = -4.665063509Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.334936491, -4.665063509}
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