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Simplifying 16x2 + 14x + 1 = 0 Reorder the terms: 1 + 14x + 16x2 = 0 Solving 1 + 14x + 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'. 0.0625 + 0.875x + x2 = 0 Move the constant term to the right: Add '-0.0625' to each side of the equation. 0.0625 + 0.875x + -0.0625 + x2 = 0 + -0.0625 Reorder the terms: 0.0625 + -0.0625 + 0.875x + x2 = 0 + -0.0625 Combine like terms: 0.0625 + -0.0625 = 0.0000 0.0000 + 0.875x + x2 = 0 + -0.0625 0.875x + x2 = 0 + -0.0625 Combine like terms: 0 + -0.0625 = -0.0625 0.875x + x2 = -0.0625 The x term is 0.875x. Take half its coefficient (0.4375). Square it (0.19140625) and add it to both sides. Add '0.19140625' to each side of the equation. 0.875x + 0.19140625 + x2 = -0.0625 + 0.19140625 Reorder the terms: 0.19140625 + 0.875x + x2 = -0.0625 + 0.19140625 Combine like terms: -0.0625 + 0.19140625 = 0.12890625 0.19140625 + 0.875x + x2 = 0.12890625 Factor a perfect square on the left side: (x + 0.4375)(x + 0.4375) = 0.12890625 Calculate the square root of the right side: 0.359035165 Break this problem into two subproblems by setting (x + 0.4375) equal to 0.359035165 and -0.359035165.Subproblem 1
x + 0.4375 = 0.359035165 Simplifying x + 0.4375 = 0.359035165 Reorder the terms: 0.4375 + x = 0.359035165 Solving 0.4375 + x = 0.359035165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = 0.359035165 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = 0.359035165 + -0.4375 x = 0.359035165 + -0.4375 Combine like terms: 0.359035165 + -0.4375 = -0.078464835 x = -0.078464835 Simplifying x = -0.078464835Subproblem 2
x + 0.4375 = -0.359035165 Simplifying x + 0.4375 = -0.359035165 Reorder the terms: 0.4375 + x = -0.359035165 Solving 0.4375 + x = -0.359035165 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.4375' to each side of the equation. 0.4375 + -0.4375 + x = -0.359035165 + -0.4375 Combine like terms: 0.4375 + -0.4375 = 0.0000 0.0000 + x = -0.359035165 + -0.4375 x = -0.359035165 + -0.4375 Combine like terms: -0.359035165 + -0.4375 = -0.796535165 x = -0.796535165 Simplifying x = -0.796535165Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.078464835, -0.796535165}
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