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Simplifying 16x2 + -40x + -65 = 0 Reorder the terms: -65 + -40x + 16x2 = 0 Solving -65 + -40x + 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'. -4.0625 + -2.5x + x2 = 0 Move the constant term to the right: Add '4.0625' to each side of the equation. -4.0625 + -2.5x + 4.0625 + x2 = 0 + 4.0625 Reorder the terms: -4.0625 + 4.0625 + -2.5x + x2 = 0 + 4.0625 Combine like terms: -4.0625 + 4.0625 = 0.0000 0.0000 + -2.5x + x2 = 0 + 4.0625 -2.5x + x2 = 0 + 4.0625 Combine like terms: 0 + 4.0625 = 4.0625 -2.5x + x2 = 4.0625 The x term is -2.5x. Take half its coefficient (-1.25). Square it (1.5625) and add it to both sides. Add '1.5625' to each side of the equation. -2.5x + 1.5625 + x2 = 4.0625 + 1.5625 Reorder the terms: 1.5625 + -2.5x + x2 = 4.0625 + 1.5625 Combine like terms: 4.0625 + 1.5625 = 5.625 1.5625 + -2.5x + x2 = 5.625 Factor a perfect square on the left side: (x + -1.25)(x + -1.25) = 5.625 Calculate the square root of the right side: 2.371708245 Break this problem into two subproblems by setting (x + -1.25) equal to 2.371708245 and -2.371708245.Subproblem 1
x + -1.25 = 2.371708245 Simplifying x + -1.25 = 2.371708245 Reorder the terms: -1.25 + x = 2.371708245 Solving -1.25 + x = 2.371708245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = 2.371708245 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = 2.371708245 + 1.25 x = 2.371708245 + 1.25 Combine like terms: 2.371708245 + 1.25 = 3.621708245 x = 3.621708245 Simplifying x = 3.621708245Subproblem 2
x + -1.25 = -2.371708245 Simplifying x + -1.25 = -2.371708245 Reorder the terms: -1.25 + x = -2.371708245 Solving -1.25 + x = -2.371708245 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '1.25' to each side of the equation. -1.25 + 1.25 + x = -2.371708245 + 1.25 Combine like terms: -1.25 + 1.25 = 0.00 0.00 + x = -2.371708245 + 1.25 x = -2.371708245 + 1.25 Combine like terms: -2.371708245 + 1.25 = -1.121708245 x = -1.121708245 Simplifying x = -1.121708245Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.621708245, -1.121708245}
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