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Simplifying -16x2 + -17x + 280 = 0 Reorder the terms: 280 + -17x + -16x2 = 0 Solving 280 + -17x + -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'. -17.5 + 1.0625x + x2 = 0 Move the constant term to the right: Add '17.5' to each side of the equation. -17.5 + 1.0625x + 17.5 + x2 = 0 + 17.5 Reorder the terms: -17.5 + 17.5 + 1.0625x + x2 = 0 + 17.5 Combine like terms: -17.5 + 17.5 = 0.0 0.0 + 1.0625x + x2 = 0 + 17.5 1.0625x + x2 = 0 + 17.5 Combine like terms: 0 + 17.5 = 17.5 1.0625x + x2 = 17.5 The x term is 1.0625x. Take half its coefficient (0.53125). Square it (0.2822265625) and add it to both sides. Add '0.2822265625' to each side of the equation. 1.0625x + 0.2822265625 + x2 = 17.5 + 0.2822265625 Reorder the terms: 0.2822265625 + 1.0625x + x2 = 17.5 + 0.2822265625 Combine like terms: 17.5 + 0.2822265625 = 17.7822265625 0.2822265625 + 1.0625x + x2 = 17.7822265625 Factor a perfect square on the left side: (x + 0.53125)(x + 0.53125) = 17.7822265625 Calculate the square root of the right side: 4.216897742 Break this problem into two subproblems by setting (x + 0.53125) equal to 4.216897742 and -4.216897742.Subproblem 1
x + 0.53125 = 4.216897742 Simplifying x + 0.53125 = 4.216897742 Reorder the terms: 0.53125 + x = 4.216897742 Solving 0.53125 + x = 4.216897742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + x = 4.216897742 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = 4.216897742 + -0.53125 x = 4.216897742 + -0.53125 Combine like terms: 4.216897742 + -0.53125 = 3.685647742 x = 3.685647742 Simplifying x = 3.685647742Subproblem 2
x + 0.53125 = -4.216897742 Simplifying x + 0.53125 = -4.216897742 Reorder the terms: 0.53125 + x = -4.216897742 Solving 0.53125 + x = -4.216897742 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.53125' to each side of the equation. 0.53125 + -0.53125 + x = -4.216897742 + -0.53125 Combine like terms: 0.53125 + -0.53125 = 0.00000 0.00000 + x = -4.216897742 + -0.53125 x = -4.216897742 + -0.53125 Combine like terms: -4.216897742 + -0.53125 = -4.748147742 x = -4.748147742 Simplifying x = -4.748147742Solution
The solution to the problem is based on the solutions from the subproblems. x = {3.685647742, -4.748147742}
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