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Simplifying -16x2 + -21x + 255 = 0 Reorder the terms: 255 + -21x + -16x2 = 0 Solving 255 + -21x + -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'. -15.9375 + 1.3125x + x2 = 0 Move the constant term to the right: Add '15.9375' to each side of the equation. -15.9375 + 1.3125x + 15.9375 + x2 = 0 + 15.9375 Reorder the terms: -15.9375 + 15.9375 + 1.3125x + x2 = 0 + 15.9375 Combine like terms: -15.9375 + 15.9375 = 0.0000 0.0000 + 1.3125x + x2 = 0 + 15.9375 1.3125x + x2 = 0 + 15.9375 Combine like terms: 0 + 15.9375 = 15.9375 1.3125x + x2 = 15.9375 The x term is 1.3125x. Take half its coefficient (0.65625). Square it (0.4306640625) and add it to both sides. Add '0.4306640625' to each side of the equation. 1.3125x + 0.4306640625 + x2 = 15.9375 + 0.4306640625 Reorder the terms: 0.4306640625 + 1.3125x + x2 = 15.9375 + 0.4306640625 Combine like terms: 15.9375 + 0.4306640625 = 16.3681640625 0.4306640625 + 1.3125x + x2 = 16.3681640625 Factor a perfect square on the left side: (x + 0.65625)(x + 0.65625) = 16.3681640625 Calculate the square root of the right side: 4.045758775 Break this problem into two subproblems by setting (x + 0.65625) equal to 4.045758775 and -4.045758775.Subproblem 1
x + 0.65625 = 4.045758775 Simplifying x + 0.65625 = 4.045758775 Reorder the terms: 0.65625 + x = 4.045758775 Solving 0.65625 + x = 4.045758775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65625' to each side of the equation. 0.65625 + -0.65625 + x = 4.045758775 + -0.65625 Combine like terms: 0.65625 + -0.65625 = 0.00000 0.00000 + x = 4.045758775 + -0.65625 x = 4.045758775 + -0.65625 Combine like terms: 4.045758775 + -0.65625 = 3.389508775 x = 3.389508775 Simplifying x = 3.389508775Subproblem 2
x + 0.65625 = -4.045758775 Simplifying x + 0.65625 = -4.045758775 Reorder the terms: 0.65625 + x = -4.045758775 Solving 0.65625 + x = -4.045758775 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.65625' to each side of the equation. 0.65625 + -0.65625 + x = -4.045758775 + -0.65625 Combine like terms: 0.65625 + -0.65625 = 0.00000 0.00000 + x = -4.045758775 + -0.65625 x = -4.045758775 + -0.65625 Combine like terms: -4.045758775 + -0.65625 = -4.702008775 x = -4.702008775 Simplifying x = -4.702008775Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.389508775, -4.702008775}
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