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Simplifying 16x2 + 220x + 77 = 0 Reorder the terms: 77 + 220x + 16x2 = 0 Solving 77 + 220x + 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'. 4.8125 + 13.75x + x2 = 0 Move the constant term to the right: Add '-4.8125' to each side of the equation. 4.8125 + 13.75x + -4.8125 + x2 = 0 + -4.8125 Reorder the terms: 4.8125 + -4.8125 + 13.75x + x2 = 0 + -4.8125 Combine like terms: 4.8125 + -4.8125 = 0.0000 0.0000 + 13.75x + x2 = 0 + -4.8125 13.75x + x2 = 0 + -4.8125 Combine like terms: 0 + -4.8125 = -4.8125 13.75x + x2 = -4.8125 The x term is 13.75x. Take half its coefficient (6.875). Square it (47.265625) and add it to both sides. Add '47.265625' to each side of the equation. 13.75x + 47.265625 + x2 = -4.8125 + 47.265625 Reorder the terms: 47.265625 + 13.75x + x2 = -4.8125 + 47.265625 Combine like terms: -4.8125 + 47.265625 = 42.453125 47.265625 + 13.75x + x2 = 42.453125 Factor a perfect square on the left side: (x + 6.875)(x + 6.875) = 42.453125 Calculate the square root of the right side: 6.515606265 Break this problem into two subproblems by setting (x + 6.875) equal to 6.515606265 and -6.515606265.Subproblem 1
x + 6.875 = 6.515606265 Simplifying x + 6.875 = 6.515606265 Reorder the terms: 6.875 + x = 6.515606265 Solving 6.875 + x = 6.515606265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.875' to each side of the equation. 6.875 + -6.875 + x = 6.515606265 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + x = 6.515606265 + -6.875 x = 6.515606265 + -6.875 Combine like terms: 6.515606265 + -6.875 = -0.359393735 x = -0.359393735 Simplifying x = -0.359393735Subproblem 2
x + 6.875 = -6.515606265 Simplifying x + 6.875 = -6.515606265 Reorder the terms: 6.875 + x = -6.515606265 Solving 6.875 + x = -6.515606265 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-6.875' to each side of the equation. 6.875 + -6.875 + x = -6.515606265 + -6.875 Combine like terms: 6.875 + -6.875 = 0.000 0.000 + x = -6.515606265 + -6.875 x = -6.515606265 + -6.875 Combine like terms: -6.515606265 + -6.875 = -13.390606265 x = -13.390606265 Simplifying x = -13.390606265Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.359393735, -13.390606265}
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