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Simplifying 16x2 + 30x + 5 = 0 Reorder the terms: 5 + 30x + 16x2 = 0 Solving 5 + 30x + 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'. 0.3125 + 1.875x + x2 = 0 Move the constant term to the right: Add '-0.3125' to each side of the equation. 0.3125 + 1.875x + -0.3125 + x2 = 0 + -0.3125 Reorder the terms: 0.3125 + -0.3125 + 1.875x + x2 = 0 + -0.3125 Combine like terms: 0.3125 + -0.3125 = 0.0000 0.0000 + 1.875x + x2 = 0 + -0.3125 1.875x + x2 = 0 + -0.3125 Combine like terms: 0 + -0.3125 = -0.3125 1.875x + x2 = -0.3125 The x term is 1.875x. Take half its coefficient (0.9375). Square it (0.87890625) and add it to both sides. Add '0.87890625' to each side of the equation. 1.875x + 0.87890625 + x2 = -0.3125 + 0.87890625 Reorder the terms: 0.87890625 + 1.875x + x2 = -0.3125 + 0.87890625 Combine like terms: -0.3125 + 0.87890625 = 0.56640625 0.87890625 + 1.875x + x2 = 0.56640625 Factor a perfect square on the left side: (x + 0.9375)(x + 0.9375) = 0.56640625 Calculate the square root of the right side: 0.752599661 Break this problem into two subproblems by setting (x + 0.9375) equal to 0.752599661 and -0.752599661.Subproblem 1
x + 0.9375 = 0.752599661 Simplifying x + 0.9375 = 0.752599661 Reorder the terms: 0.9375 + x = 0.752599661 Solving 0.9375 + x = 0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = 0.752599661 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = 0.752599661 + -0.9375 x = 0.752599661 + -0.9375 Combine like terms: 0.752599661 + -0.9375 = -0.184900339 x = -0.184900339 Simplifying x = -0.184900339Subproblem 2
x + 0.9375 = -0.752599661 Simplifying x + 0.9375 = -0.752599661 Reorder the terms: 0.9375 + x = -0.752599661 Solving 0.9375 + x = -0.752599661 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '-0.9375' to each side of the equation. 0.9375 + -0.9375 + x = -0.752599661 + -0.9375 Combine like terms: 0.9375 + -0.9375 = 0.0000 0.0000 + x = -0.752599661 + -0.9375 x = -0.752599661 + -0.9375 Combine like terms: -0.752599661 + -0.9375 = -1.690099661 x = -1.690099661 Simplifying x = -1.690099661Solution
The solution to the problem is based on the solutions from the subproblems. x = {-0.184900339, -1.690099661}
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