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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 = 4.665063509 x = 4.665063509 Simplifying x = 4.665063509Subproblem 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 = 0.334936491 x = 0.334936491 Simplifying x = 0.334936491Solution
The solution to the problem is based on the solutions from the subproblems. x = {4.665063509, 0.334936491}
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